← Index: Syllogism — Concepts, Shortcuts & Practice BankChapter 1

Study Guide · Chapter 1

Syllogism — Complete Guide

Free study material · concepts, shortcuts & solved questions

Introduction to Syllogism
Practice Questions — Statement Types & Conversion
The Venn Diagram Method
Practice Questions — Venn Diagram Method
The Rules-Based (Shortcut) Method
Practice Questions — Rules-Based Method
Complementary Pairs — Either-Or Conclusions
Practice Questions — Either-Or / Complementary Pairs
Possibility-Based Questions
Practice Questions — Possibility-Based
Three-Statement and Four-Statement Syllogisms
Practice Questions — Three & Four Statement Syllogisms
Coded (Symbolic) Syllogism
Practice Questions — Coded Syllogism
The Standard Exam Format — Statement & Numbered Conclusions
Practice Questions — Standard Format Practice
Common Traps Examiners Use
Practice Questions — Spot the Trap
Step-by-Step Solving Framework for Exam Speed
Practice Questions — Mixed Review (Full Framework)
Final Practice Set — 25 Mixed Questions
Consolidated Answer Key — Final Practice Set

1. Introduction to Syllogism

What Syllogism Tests

Syllogism is a Reasoning-section topic that tests your ability to judge whether a conclusion logically follows from one or more given statements, without relying on real-world knowledge or personal opinion. You must treat every statement as true exactly as written, even if it sounds factually odd ("All cats are elephants" must be accepted as true for the purposes of the question), and work out purely on the basis of logical structure which conclusions are forced to be true.

This makes Syllogism a test of disciplined, mechanical reasoning rather than general knowledge — which is exactly why it is scorable: once you master the rules, results become consistent and fast.

Why It Is High-Weightage

SSC CGL, CHSL, MTS and GD Reasoning sections almost always carry 3 to 5 Syllogism questions in every shift.
RRB NTPC and Group D exams are equally generous with this topic, often combining it with coded/symbolic variations.
Unlike puzzles or series, Syllogism has a small, fixed rule-set — so with practice, accuracy can reach 100% and speed can reach under 30 seconds per question.
It is one of the very few reasoning topics where the "logic" is completely learnable from a table, rather than requiring flexible improvisation.

The Four Categorical Statement Types

Every syllogism statement in these exams falls into one of four standard forms, traditionally labelled A, E, I, O:

Code	Form	Example	Meaning
A	Universal Affirmative	All A are B	Every member of A is also a member of B.
E	Universal Negative	No A is B	No member of A is a member of B (A and B are fully separate).
I	Particular Affirmative	Some A are B	At least one member of A is also a member of B.
O	Particular Negative	Some A are not B	At least one member of A is NOT a member of B.

Convention used throughout this book: every class named in a statement (A, B, C ...) is assumed to be non-empty — that is, at least one member of that class exists. This is the standard "existential import" assumption used by SSC and RRB exams and is essential for the subalternation rule explained below.

Immediate Inferences (Conversion) for Each Type

An "immediate inference" is a conclusion drawn from a single statement alone, without needing a second statement. The most important immediate inference is conversion — swapping the subject and predicate.

Statement	Valid Conversion	Notes
All A are B (A)	Some B are A	The A-type statement can NEVER be fully reversed to "All B are A" — that is the single most common trap in this topic.
No A is B (E)	No B is A	E-type statements convert simply and fully — this is one of the few completely safe reversals.
Some A are B (I)	Some B are A	I-type statements always convert simply — swapping the order changes nothing.
Some A are not B (O)	NO valid conversion	This is the only type with absolutely no valid converse. "Some erasers are not pens" can NEVER be concluded from "Some pens are not erasers."

Subalternation (a second useful immediate inference)

Because every class is assumed non-empty, a universal statement always implies its matching particular statement of the same quality:

"All A are B" implies "Some A are B" (and, by conversion, "Some B are A").
"No A is B" implies "Some A are not B" (and, by conversion, "No B is A", which implies "Some B are not A").

This single rule quietly makes many exam "Both conclusions follow" answers correct, and is frequently missed by students who stop after finding just the stronger conclusion.

Speed Tip:

Memorise this 4-row conversion table cold — it is tested directly (single-statement questions) and is also the foundation of every two-statement rule you will learn next.

The only "unsafe" statement type is O (Some ... are not ...). If you ever see a conclusion that reverses an O-type statement, it is almost certainly the trap answer.

2. Practice Questions — Statement Types & Conversion

Q1. Statements: All roses are flowers.
Conclusions: I. Some flowers are roses. II. All flowers are roses.
(A) Only I follows (B) Only II follows (C) Both I and II follow (D) Neither I nor II follows
Answer: (A) Only I follows
Explanation: ‘All A are B’ always gives the valid converse ‘Some B are A’. So Some flowers are roses is definitely true. ‘All flowers are roses’ reverses the statement completely and is not warranted — this is the classic illicit-conversion trap for A-type statements.

Q2. Statements: No cat is a dog.
Conclusions: I. No dog is a cat. II. Some cats are dogs.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: ‘No A is B’ converts simply and validly to ‘No B is A’, so I is true. II directly contradicts the given statement, so it is false.

Q3. Statements: Some students are boys.
Conclusions: I. Some boys are students. II. All students are boys.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: ‘Some A are B’ converts validly to ‘Some B are A’, so I follows. II is far stronger than what is given and does not follow.

Q4. Statements: Some engineers are not doctors.
Conclusions: I. Some doctors are not engineers. II. No engineer is a doctor.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: An O-type statement (‘Some A are not B’) has NO valid conversion at all. Concluding ‘Some doctors are not engineers’ is the classic illicit-conversion trap, and ‘No engineer is a doctor’ is far too strong. Neither follows.

Q5. Statements: All tigers are lions.
Conclusions: Which of the following is a valid immediate inference?
(A) All lions are tigers (B) Some lions are tigers (C) No lion is a tiger (D) Some lions are not tigers
Answer: (B) Some lions are tigers
Explanation: The valid converse of an A-type statement is the corresponding I-type statement: Some lions are tigers.

Q6. Which pair correctly represents a Universal Negative followed by a Particular Affirmative?
(A) All A are B, No A is B (B) No A is B, Some A are B (C) Some A are B, All A are B (D) Some A are not B, All A are B
Answer: (B) No A is B, Some A are B
Explanation: Universal Negative = ‘No A is B’ (E); Particular Affirmative = ‘Some A are B’ (I). Option B lists them in that order.

Q7. ‘Some fruits are not mangoes’ is which type of categorical statement?
(A) Universal Affirmative (A) (B) Universal Negative (E) (C) Particular Affirmative (I) (D) Particular Negative (O)
Answer: (D) Particular Negative (O)
Explanation: ‘Some X are not Y’ is the Particular Negative (O) statement.

Q8. Statements: Some books are pens.
Conclusions: Which conclusion is definitely true?
(A) All pens are books (B) No pen is a book (C) Some pens are books (D) All books are pens
Answer: (C) Some pens are books
Explanation: The valid converse of ‘Some A are B’ is ‘Some B are A’, i.e. Some pens are books.

Q9. Statements: No mobile is a laptop.
Conclusions: I. No laptop is a mobile. II. Some mobiles are laptops.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: E-type statements convert simply and validly, so ‘No laptop is a mobile’ follows. II contradicts the given statement.

Q10. Which statement type has NO valid converse at all?
(A) All A are B (B) No A is B (C) Some A are B (D) Some A are not B
Answer: (D) Some A are not B
Explanation: Only the O-type statement (‘Some A are not B’) has no valid simple conversion — attempting to convert it is a very common exam trap.

3. The Venn Diagram Method

The Venn diagram method is the most intuitive way to solve syllogisms: you draw every diagram that could possibly satisfy the given statements, and a conclusion is "definitely true" only if it holds in EVERY one of those diagrams.

Drawing All Possible Diagrams

For two statements sharing a common (middle) term, follow this procedure:

Step 1 — Draw a circle for each class mentioned (usually 2 or 3 circles).
Step 2 — For each statement, draw every diagram consistent with it. A statement like "All A are B" has only ONE possible diagram (A fully inside B). A statement like "Some A are B" has THREE possible diagrams: partial overlap, A fully inside B, or B fully inside A — since "some" only guarantees at least one common element, not the exact extent of overlap.
Step 3 — Combine every diagram of statement 1 with every diagram of statement 2 that is mutually consistent, producing the full set of possible combined diagrams.
Step 4 — Check each proposed conclusion against every combined diagram: if it is true in ALL of them, it is "definitely true"; if it is true in AT LEAST ONE but not all, it is "possibly true"; if it is true in NONE, it is "definitely false".

Worked Example

Statements: (I) All doctors are engineers. (II) No engineer is a teacher.

Statement I has only one diagram: the Doctors circle sits fully inside the Engineers circle. Statement II has only one diagram: the Engineers circle and the Teachers circle do not touch at all. Combining these forces the Doctors circle to also be completely separate from the Teachers circle in every possible combined diagram.

Conclusion check: "No doctor is a teacher" is true in the only possible diagram, so it is DEFINITELY TRUE. By subalternation, "Some doctors are not teachers" is also definitely true.

Definitely True vs Possibly True

Term	Meaning	How exams phrase it
Definitely true	Holds in every valid diagram	"...follows" / "...can be concluded"
Definitely false	Holds in no valid diagram	"...cannot be concluded" / "is not a possibility"
Possibly true	Holds in at least one but not all valid diagrams	"...is a possibility" (see Chapter 5)

Speed Tip:

You rarely need to draw all three diagrams for a "Some" statement from scratch in the exam — instead, learn the 16-row Rule Table in Chapter 3, which encodes the outcome of every possible Venn combination. Use Venn diagrams only to double-check tricky either-or or possibility questions.

4. Practice Questions — Venn Diagram Method

Q11. Statements: I. Some books are pens. II. All pens are tables.
Conclusions: I. Some books are tables. II. All tables are books.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Venn check: draw the Some-Books/Pens overlap; since all Pens lie inside Tables, the overlapping portion of Books also lies inside Tables. So Some books are tables is definite. ‘All tables are books’ is far too strong — it does not follow.

Q12. Statements: I. All doctors are engineers. II. No engineer is a teacher.
Conclusions: I. No doctor is a teacher. II. Some doctors are not teachers.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Every possible Venn diagram places the Doctors circle fully inside Engineers, which is fully separate from Teachers — so Doctors and Teachers never touch: No doctor is a teacher (I) is definite. Since a universal negative conclusion always yields the matching particular negative (assuming the class is non-empty), II also follows. Both follow.

Q13. Statements: I. Some flowers are roses. II. No rose is a plant.
Conclusions: I. Some flowers are not plants. II. No flower is a plant.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: The Flowers-Roses overlap lies inside Roses, which is completely outside Plants. So that overlapping part of Flowers is definitely outside Plants: Some flowers are not plants (I) is definite. II is too strong — other flowers (outside the overlap) could still be plants.

Q14. Statements: I. All chairs are tables. II. Some tables are boxes.
Conclusions: I. Some chairs are boxes. II. Some boxes are chairs.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Chairs sit somewhere inside Tables, but the ‘Some tables that are boxes’ portion may or may not include the Chairs region — multiple Venn diagrams are possible, some with overlap and some without. Since I and II say the same thing in different words, and neither is forced, neither follows.

Q15. Statements: I. All pilots are drivers. II. All drivers are humans.
Conclusions: I. All pilots are humans. II. Some humans are pilots.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Pilots ⊆ Drivers ⊆ Humans in every possible diagram, so All pilots are humans (I) is definite. Its valid converse, Some humans are pilots (II), also follows. Both follow.

Q16. Statements: I. No actor is a singer. II. All singers are artists.
Conclusions: I. Some artists are not actors. II. No artist is an actor.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Singers lie fully inside Artists but fully outside Actors, so that Singer-portion of Artists is definitely not Actors: Some artists are not actors (I) is definite. II is too strong — non-singer artists could still be actors.

Q17. Statements: I. No tiger is a lion. II. Some lions are wild animals.
Conclusions: I. Some wild animals are not tigers. II. No wild animal is a tiger.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: The Lions that are Wild animals are, by the first statement, definitely not Tigers. So Some wild animals are not tigers (I) is definite; II is too strong to be guaranteed.

Q18. Statements: I. Some pens are pencils. II. Some pencils are stationery.
Conclusions: I. Some pens are stationery. II. No pen is stationery.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Drawing the Venn diagrams shows the Pens-that-are-Pencils and the Pencils-that-are-Stationery need not be the same pencils, so neither I nor II is individually forced. But I and II are an exact contradictory pair (Some / No) about the same two terms (Pens, Stationery) with nothing else known — in every possible diagram at least one of them must be true. Hence Either I or II follows.

Q19. Statements: I. All mangoes are fruits. II. Some fruits are apples.
Conclusions: I. Some mangoes are apples. II. All apples are mangoes.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Mangoes sit somewhere inside Fruits, but the ‘apple’ portion of Fruits may lie entirely outside the Mango region in some diagrams — so I is not guaranteed. II is far too strong. Neither follows.

Q20. Statements: I. Some doctors are not engineers. II. All engineers are teachers.
Conclusions: I. Some doctors are teachers. II. Some doctors are not teachers.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: The doctors who are not engineers have no fixed relationship to Teachers at all — they could be teachers or not, independent of the Engineer-Teacher link. Multiple diagrams exist; neither conclusion is forced. (Common trap: assuming these doctors must therefore also miss being teachers.)

Q21. Statements: I. No rivers are lakes. II. No lakes are water bodies.
Conclusions: I. No river is a water body. II. Some rivers are water bodies.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Chaining two negative statements (No-No) never fixes the relation between the two end terms — Rivers and Water bodies could overlap fully, partly, or not at all across different diagrams. Since I and II form the exact contradictory (No/Some) pair about the same terms, Either I or II follows, even though neither is individually certain.

5. The Rules-Based (Shortcut) Method

Drawing Venn diagrams for every question is reliable but slow. Once you understand WHY the diagrams give the results they do, you can skip straight to a memorised rule table — this is how toppers solve two-statement syllogisms in under 20 seconds.

The Master Rule Table

This table applies whenever two statements share one common (middle) term B, arranged as a chain: Statement 1 relates A to B, Statement 2 relates B to C. The conclusion, if any, always relates the two EXTREME terms, A and C.

Statement 1	Statement 2	Valid Conclusion (about extreme terms)
All A are B	All B are C	All A are C (+ Some C are A)
All A are B	No B is C	No A is C (+ Some A are not C)
All A are B	Some B are C	No definite conclusion
All A are B	Some B are not C	No definite conclusion
No A is B	All B are C	Some C are not A
No A is B	No B is C	No definite conclusion
No A is B	Some B are C	Some C are not A
No A is B	Some B are not C	No definite conclusion
Some A are B	All B are C	Some A are C (+ Some C are A)
Some A are B	No B is C	Some A are not C
Some A are B	Some B are C	No definite conclusion
Some A are B	Some B are not C	No definite conclusion
Some A are not B	All B are C	No definite conclusion
Some A are not B	No B is C	No definite conclusion
Some A are not B	Some B are C	No definite conclusion
Some A are not B	Some B are not C	No definite conclusion

Rows 1, 2, 5, 7, 9 and 10 give a definite conclusion — these are the only six genuinely "productive" combinations.
Every other combination (the ten "No definite conclusion" rows) leaves the A–C relationship completely open — but note Chapter 4, since some of these unlock a valid "either-or" conclusion instead.
Whenever a conclusion is of type All or No, remember to also check subalternation for a second valid conclusion (the matching Some / Some-not statement).
Whenever a conclusion is of type All or Some, remember to also check its valid converse for a second valid conclusion.

Using the Table — Step by Step

1. Identify the common (middle) term shared by both statements.
2. Rewrite both statements, if needed, so the middle term is the PREDICATE of statement 1 and the SUBJECT of statement 2 (a proper chain: A→B, B→C).
3. Look up the row matching the type of statement 1 and statement 2.
4. Read off the conclusion, remembering to also apply conversion/subalternation for any extra valid conclusions.
5. If the table gives "No definite conclusion", check whether the offered conclusions form a valid either-or pair (Chapter 4) before finally rejecting them.

Important Warning:

The table above ONLY applies when the middle term is the predicate of statement 1 and the subject of statement 2 (or vice versa after reordering). If the middle term is the PREDICATE in BOTH statements (e.g. "All lions are carnivores", "All tigers are carnivores") or the SUBJECT in both, the extreme terms have NO forced relationship at all — this is one of the most common traps (see Chapter 6 and Chapter 9).

6. Practice Questions — Rules-Based Method

Q22. Statements: I. All actors are singers. II. Some singers are not artists.
Conclusions: I. Some actors are artists. II. Some actors are not artists.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: All + Some-not = No definite conclusion between the extreme terms. The singers who are not artists may or may not include any actors. Both I and II remain merely possible, not certain.

Q23. Statements: I. No bags are boxes. II. Some boxes are not containers.
Conclusions: I. Some bags are containers. II. Some bags are not containers.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: No + Some-not = No definite conclusion. The boxes that are not containers tell us nothing about bags, since bags and boxes are already fully separate. Both remain undetermined.

Q24. Statements: I. Some mobiles are laptops. II. Some laptops are not gadgets.
Conclusions: I. Some mobiles are not gadgets. II. Some mobiles are gadgets.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: Some + Some-not = No definite conclusion. The laptops that are not gadgets need not be the same laptops that are mobiles, so nothing certain follows about mobiles and gadgets.

Q25. Statements: I. Some chairs are not tables. II. No table is furniture.
Conclusions: I. Some chairs are not furniture. II. Some chairs are furniture.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: Some-not + No = No definite conclusion. Knowing some chairs are outside Tables, and Tables are entirely outside Furniture, tells us nothing about those chairs and Furniture.

Q26. Statements: I. Some rats are not cats. II. Some cats are animals.
Conclusions: I. Some rats are animals. II. Some rats are not animals.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: Some-not + Some = No definite conclusion. The cats that are animals need not overlap with the rats that are not cats, so the rat-animal relation stays open.

Q27. Statements: I. Some soldiers are not officers. II. Some officers are not men.
Conclusions: I. Some soldiers are not men. II. Some soldiers are men.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: Rule table: Some-not + Some-not = No definite conclusion. Both conclusions remain merely possible.

Q28. Statements: I. All pens are pencils. II. All pencils are stationery.
Conclusions: I. All pens are stationery. II. Some stationery are pens.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Rule table: All + All = All (Pens ⊆ Stationery), so I is definite. Its valid converse, Some stationery are pens, also follows. Both follow.

Q29. Statements: I. All roses are flowers. II. No flower is a weed.
Conclusions: I. No rose is a weed. II. Some roses are not weeds.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Rule table: All + No = No (No rose is a weed), which is definite. A universal negative conclusion always yields the matching particular negative, so II also follows. Both follow.

Q30. Statements: I. No pilot is a driver. II. All drivers are humans.
Conclusions: I. Some humans are not pilots. II. All humans are not pilots.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table: No + All = Some (of the predicate class) are not (the subject class), i.e. Some humans are not pilots — definite. II (‘No human is a pilot’) is far stronger and not guaranteed, since humans outside the ‘driver’ group could still be pilots.

Q31. Statements: I. No mangoes are apples. II. Some apples are fruits.
Conclusions: I. Some fruits are not mangoes. II. No fruit is a mango.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table: No + Some = Some (of the predicate class) are not (the subject class): Some fruits are not mangoes is definite. II is too strong to be guaranteed.

Q32. Statements: I. Some teachers are doctors. II. All doctors are engineers.
Conclusions: I. Some teachers are engineers. II. All engineers are teachers.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table: Some + All = Some (of the subject class) are (the predicate class): Some teachers are engineers is definite. II is far too strong and unwarranted.

Q33. Statements: I. Some students are boys. II. No boy is a girl.
Conclusions: I. Some students are not girls. II. All students are not girls.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table: Some + No = Some (of the subject class) are not (the predicate class): Some students are not girls is definite. II (‘No student is a girl’) is too strong — other students could still be girls.

7. Complementary Pairs — Either-Or Conclusions

Sometimes two conclusions that individually look invalid actually combine into a valid "Either I or II follows" answer. This happens when the two conclusions are strict logical opposites of each other, and the given statements leave genuinely no way to decide which one is true — yet one of them MUST be true.

The Two Approved Complementary Pairs

By exam convention, the either-or test is applied ONLY to these two pairs of conclusions, and only when they concern the exact same subject and predicate in the exact same order:

Approved Pair	Why it works
All A are B ⇔ Some A are not B	These are strict contradictories — exactly one must be true for any non-empty class A.
No A is B ⇔ Some A are B	These are also strict contradictories — exactly one must always be true.

A Some / Some-not pair is NOT treated as either-or under exam convention, even though both cannot be false at once — this distinction is tested directly (see Q44 and Q96).
The two conclusions MUST run in the same subject-predicate direction. "All A are B" paired with "Some B are not A" is NOT a valid either-or pair — the direction is reversed.

The Exact Test to Apply

Step 1 — Check whether either conclusion follows individually and definitely from the rule table. If yes, that single conclusion is the answer — do NOT mark either-or, even though it happens to also be trivially true.
Step 2 — If neither follows individually, check whether the two conclusions form one of the two approved pairs, in the same direction, about the same two terms.
Step 3 — If both Step 1 and Step 2 conditions are met (neither follows alone, AND they form an approved pair), the answer is "Either I or II follows."

Worked Example

Statements: Some doctors are engineers. All engineers are graduates.

The rule table (Some+All) proves "Some doctors are graduates" — but this exact statement is usually not among the offered conclusions. Instead the options ask about "All doctors are graduates" and "Some doctors are not graduates." Neither is individually provable: it is possible that every doctor happens to be a graduate (no doctor left over), and it is equally possible that some doctors are not. Since these two options are the approved All/Some-not pair and neither is provable alone, the correct answer is Either I or II follows.

Speed Tip:

Whenever you see the same two terms paired as (All / Some-not) or (No / Some) in the conclusions, first check the rule table result. If the table gives a clean, stronger single answer (or if one option directly matches a proven fact), pick that — never default to "either-or" as a shortcut.

8. Practice Questions — Either-Or / Complementary Pairs

Q34. Statements: I. Some doctors are engineers. II. All engineers are graduates.
Conclusions: I. All doctors are graduates. II. Some doctors are not graduates.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: The rule table (Some+All) guarantees only ‘Some doctors are graduates’ — definite, but not directly an option here. Whether ALL doctors happen to be graduates, or SOME are not, is left open by the premises; these are exactly complementary (one must be true). Either I or II follows.

Q35. Statements: I. Some pens are pencils. II. No pencil is a marker.
Conclusions: I. No pen is a marker. II. Some pens are markers.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: The rule table (Some+No) guarantees ‘Some pens are not markers’ — definite. Whether the remaining pens are markers or not is left open, and I/II are the exact complementary (No/Some) pair. Either I or II follows.

Q36. Statements: I. Some actors are directors. II. All directors are producers.
Conclusions: I. All actors are producers. II. Some actors are not producers.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: ‘Some actors are producers’ is guaranteed, but whether this extends to ALL actors or leaves SOME actors out is undetermined — an exact All/Some-not complementary pair. Either I or II follows.

Q37. Statements: I. Some rivers are canals. II. No canal is a pond.
Conclusions: I. No river is a pond. II. Some rivers are ponds.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: ‘Some rivers are not ponds’ is guaranteed; whether any river is a pond at all is left open. I/II form the exact No/Some complementary pair. Either I or II follows.

Q38. Statements: I. All mangoes are fruits. II. Some fruits are sweet things.
Conclusions: I. Some mangoes are sweet things. II. No mango is a sweet thing.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table: All+Some = No definite conclusion, so the mango–sweet-thing relation is completely open — it could be anything from full overlap to none. Since I and II are the exact No/Some complementary pair, one of them must always be true. Either I or II follows.

Q39. Statements: I. All chairs are furniture. II. Some furniture is not wooden.
Conclusions: I. All chairs are wooden. II. Some chairs are not wooden.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table: All+Some-not = No definite conclusion — the chair–wooden relation is completely open. I and II form the exact All/Some-not complementary pair, so Either I or II follows.

Q40. Statements: I. No pilots are doctors. II. Some doctors are not surgeons.
Conclusions: I. No pilot is a surgeon. II. Some pilots are surgeons.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table: No+Some-not = No definite conclusion — the pilot–surgeon relation is completely open. I and II form the exact No/Some complementary pair, so Either I or II follows.

Q41. Statements: I. Some teachers are writers. II. Some writers are poets.
Conclusions: I. Some teachers are poets. II. No teacher is a poet.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table: Some+Some = No definite conclusion — teacher–poet relation completely open. I and II form the exact Some/No complementary pair, so Either I or II follows.

Q42. Statements: I. All doctors are engineers. II. All engineers are graduates.
Conclusions: I. All doctors are graduates. II. Some doctors are not graduates.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (A) Only I follows
Explanation: Trap: this LOOKS like an All/Some-not pair, but rule table All+All=All makes ‘All doctors are graduates’ (I) directly and definitely true. Since I is already proven, II is automatically false (it contradicts I) — this is NOT an either-or case. Only I follows.

Q43. Statements: I. Some pens are pencils. II. All pencils are erasers.
Conclusions: I. All pens are erasers. II. Some erasers are not pens.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (D) Neither I nor II follows
Explanation: Trap: I and II look like they might pair up, but they are stated in opposite directions (I is Pens→Erasers, II is Erasers→Pens) — the either-or test requires the SAME subject-predicate order in both conclusions. Rule table (Some+All) only guarantees ‘Some pens are erasers’, so neither I (too strong) nor II (unrelated direction, unproven) follows. Neither follows.

Q44. Statements: I. Some actors are singers. II. Some singers are dancers.
Conclusions: I. Some actors are dancers. II. Some actors are not dancers.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (D) Neither I nor II follows
Explanation: Trap: I and II look complementary, but a Some/Some-not pair is NOT one of the two approved either-or templates (only All/Some-not and No/Some qualify). Rule table (Some+Some) gives no definite conclusion either way. By exam convention, neither follows.

Q45. Statements: I. All keys are metals. II. No metal is wood.
Conclusions: I. No key is wood. II. Some keys are wood.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (A) Only I follows
Explanation: Trap: this looks like a No/Some either-or pair, but rule table All+No=No makes ‘No key is wood’ (I) directly and definitely true. Since I is already proven, II is automatically false — not an either-or case. Only I follows.

9. Possibility-Based Questions

A separate exam format asks not "which conclusion follows" but "which of the following is a possibility" (or "is definitely not a possibility"). These questions test whether you can tell the difference between definitely true, definitely false, and merely possible.

The Three Categories

Category	Test
Definitely true	It follows from the rule table, or it is directly restated from a given premise, or it follows by conversion/subalternation.
Definitely false (impossible)	It directly contradicts something that is definitely true.
Possibly true (a genuine possibility)	It is neither proven nor contradicted — some valid Venn diagram allows it.

How Exam-Setters Phrase These Questions

"Which of the following is a possibility?" — pick the one option that is not ruled out.
"Which of the following is definitely NOT a possibility?" — pick the one option that directly contradicts a proven fact.
"If [some extra condition] is true, which statement is a possibility?" — treat the extra condition as a THIRD premise and re-check consistency.
"Which of the following must be true?" — this is actually a definitely-true question in disguise; do not confuse it with a possibility question.

Worked Example

Statements: Some pens are pencils. No pencil is a marker. The rule table (Some+No) proves "Some pens are not markers" is definitely true. Therefore "All pens are markers" is impossible — it directly contradicts a proven fact. Meanwhile "No pen is a marker" and "Some pens are markers" remain open possibilities (in fact, they form a valid either-or pair from Chapter 4).

Speed Tip:

First work out whatever the rule table DOES prove — that becomes your yardstick. Any option that contradicts the proven fact is automatically impossible; every other option (unless it is even stronger than what's proven, like reversing to "All") is usually a live possibility.

10. Practice Questions — Possibility-Based

Q46. Statements: I. Some doctors are engineers. II. All engineers are graduates.
Conclusions: Which of the following is definitely NOT a possibility?
(A) All doctors are graduates (B) Some doctors are not graduates (C) No doctor is a graduate (D) Some doctors are graduates
Answer: (C) No doctor is a graduate
Explanation: ‘Some doctors are graduates’ is a proven, definite fact (Some+All rule). Its direct opposite, ‘No doctor is a graduate’, can therefore never be true — it is impossible. (A) and (B) are the genuine either-or possibilities, and (D) is simply the proven fact itself.

Q47. Statements: I. Some pens are pencils. II. No pencil is a marker.
Conclusions: Which of the following is definitely NOT a possibility?
(A) No pen is a marker (B) Some pens are markers (C) Some pens are not markers (D) All pens are markers
Answer: (D) All pens are markers
Explanation: ‘Some pens are not markers’ is proven (Some+No rule). This directly rules out ‘All pens are markers’, which would require every pen to be a marker. (A) and (B) remain open possibilities.

Q48. Statements: I. All actors are singers. II. Some singers are not dancers.
Conclusions: Which of the following is definitely TRUE (not merely possible)?
(A) All actors are dancers (B) No actor is a dancer (C) Some singers are not dancers (D) Some actors are dancers
Answer: (C) Some singers are not dancers
Explanation: Option (C) simply restates the given second statement, so it is certain. The actor–dancer relation itself is completely undetermined by the premises (All+Some-not rule), so (A), (B) and (D) are all merely possible, not certain.

Q49. Statements: I. No teachers are writers. II. Some writers are poets.
Conclusions: Which of the following is definitely NOT a possibility?
(A) Some poets are not teachers (B) All poets are teachers (C) No poet is a teacher (D) Some poets are teachers
Answer: (B) All poets are teachers
Explanation: ‘Some poets are not teachers’ is proven (No+Some rule). This rules out ‘All poets are teachers’, which would require every poet to be a teacher. (C) and (D) remain a valid either-or possibility pair.

Q50. Statements: I. Some boxes are bags. II. Some bags are not baskets.
Conclusions: Which of the following is definitely TRUE (not merely possible)?
(A) All boxes are baskets (B) No box is a basket (C) Some bags are not baskets (D) Some boxes are not baskets
Answer: (C) Some bags are not baskets
Explanation: Option (C) simply restates the given second statement, so it is certain. The box–basket relation is left completely open by the premises (Some+Some-not rule), so the other options are merely possible.

Q51. Statements: I. All keys are metals. II. No metal is wood.
Conclusions: Which of the following possibility is ruled out (definitely false)?
(A) No key is wood (B) Some keys are not wood (C) Some keys are wood (D) All metals are keys
Answer: (C) Some keys are wood
Explanation: ‘No key is wood’ is proven directly (All+No rule), so its contradictory, ‘Some keys are wood’, is impossible. (A) and (B) are already certain, and (D) remains an open possibility about the reverse Metal–Key relation, which the premises do not forbid.

Q52. Statements: I. Some rivers are canals. II. No canal is a pond.
Conclusions: Which of the following is NOT a possibility?
(A) All rivers are ponds (B) No river is a pond (C) Some rivers are ponds (D) Some rivers are not ponds
Answer: (A) All rivers are ponds
Explanation: ‘Some rivers are not ponds’ is proven (Some+No rule), so ‘All rivers are ponds’ is impossible. (D) is certain, and (B)/(C) form a valid open either-or pair.

Q53. Statements: I. Some mangoes are apples. II. No apple is a banana.
Conclusions: Which of the following is definitely false (not possible)?
(A) Some mangoes are not bananas (B) All mangoes are bananas (C) No mango is a banana (D) Some mangoes are bananas
Answer: (B) All mangoes are bananas
Explanation: ‘Some mangoes are not bananas’ is proven (Some+No rule), directly ruling out ‘All mangoes are bananas’. (C) and (D) remain an open either-or pair.

Q54. Statements: I. All chairs are furniture. II. Some furniture is not wooden.
Conclusions: Which of the following is definitely TRUE (a certainty, not merely a possibility)?
(A) All chairs are wooden (B) No chair is wooden (C) Some furniture is not wooden (D) Some chairs are not wooden
Answer: (C) Some furniture is not wooden
Explanation: Option (C) merely restates the given second statement, so it is certain. The chair–wooden relation itself is left fully open by the premises.

Q55. Statements: I. Some students are boys. II. All boys are athletes.
Conclusions: Which of the following is impossible given the statements?
(A) All students are athletes (B) Some students are not athletes (C) No student is an athlete (D) Some students are athletes
Answer: (C) No student is an athlete
Explanation: ‘Some students are athletes’ is proven (Some+All rule), so ‘No student is an athlete’ directly contradicts it and is impossible. (A) and (B) form an open either-or pair, and (D) is the proven fact.

11. Three-Statement and Four-Statement Syllogisms

When three or four statements are chained together (A–B, B–C, C–D ...), apply the two-statement rule table repeatedly, one link at a time, always checking whether the middle term is properly placed (predicate of one statement, subject of the next).

The Chaining Procedure

Step 1 — Combine statements 1 and 2 using the rule table to get an intermediate conclusion about A and C (if any).
Step 2 — Combine that intermediate conclusion with statement 3 to get a conclusion about A and D (if any).
Step 3 — Continue this way for a fourth statement. Also keep track of any valid conclusions from ADJACENT pairs of statements alone (e.g., statements 2 and 3), since these are frequently offered as separate conclusion options.

The Most Important Pitfall: Direction Sensitivity

A chain does NOT survive equally well in both directions:

"Some A are B" followed by any number of "All ... are ..." links STAYS valid all the way through (Some+All=Some, and this new "Some" statement can chain with the next "All" link again, and so on).
But the moment an "All" statement is followed by a "Some" statement (All+Some), the chain BREAKS — no definite conclusion crosses that link, even if every other link in the chain is a perfectly valid "All."

This single asymmetry is one of the most heavily tested pitfalls in 3-and-4-statement syllogisms — many students wrongly assume that if most links are "All", the final conclusion must also be strong.

The "Common Superset" Pitfall

When two different statements both make the SAME term their predicate (e.g. "All actors are singers" and "All dancers are singers"), the two subjects (Actors, Dancers) have NO forced relationship at all — they are simply two possibly-unrelated subsets of the same larger set. The same applies if two statements both make the same term their SUBJECT. Always check that the middle term is placed as predicate-then-subject (a genuine chain) before applying the rule table.

Speed Tip:

In a 3- or 4-statement question, don't just chain everything blindly to the extreme ends. Also check every ADJACENT pair separately — sub-chains that don't cross a broken (All+Some) link can still give a valid, scorable conclusion even when the full end-to-end chain fails.

12. Practice Questions — Three & Four Statement Syllogisms

Q56. Statements: I. All pens are pencils. II. All pencils are erasers. III. All erasers are stationery.
Conclusions: I. All pens are stationery. II. Some pencils are stationery.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Chaining All+All+All gives All pens are stationery directly (I). Separately, All pencils are erasers + All erasers are stationery gives All pencils are stationery, whose valid converse is Some stationery are pencils, so ‘Some pencils are stationery’ also follows by subalternation. Both follow.

Q57. Statements: I. All doctors are engineers. II. No engineer is a teacher. III. Some teachers are professors.
Conclusions: I. Some professors are not doctors. II. No doctor is a teacher.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Step 1: All doctors are engineers + No engineer is a teacher ⟹ No doctor is a teacher (II, definite). Step 2: treat ‘No doctor is a teacher’ with ‘Some teachers are professors’ (No+Some rule) ⟹ Some professors are not doctors (I). Both follow.

Q58. Statements: I. Some pilots are drivers. II. All drivers are humans. III. No human is a robot.
Conclusions: I. Some pilots are not robots. II. No pilot is a robot.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Step 1: Some pilots are drivers + All drivers are humans ⟹ Some pilots are humans (Some+All rule). Step 2: Some pilots are humans + No human is a robot ⟹ Some pilots are not robots (Some+No rule) — definite. II is too strong to be guaranteed.

Q59. Statements: I. All actors are singers. II. All dancers are singers. III. All singers are artists.
Conclusions: I. All actors are artists. II. All dancers are artists. III. Some actors are dancers.
(A) Only I and II follow (B) All three follow (C) Only III follows (D) None follow
Answer: (A) Only I and II follow
Explanation: Pitfall: statements 1 and 2 both make Singers the PREDICATE (Actors⊆Singers and Dancers⊆Singers) — two different subsets of the same larger set need not relate to each other at all, so III is undetermined. However, chaining each with statement 3 (All+All=All) validly gives All actors are artists (I) and All dancers are artists (II). Only I and II follow.

Q60. Statements: I. No bag is a box. II. All boxes are containers. III. Some containers are baskets.
Conclusions: I. Some containers are not bags. II. Some baskets are not bags.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Step 1: No bag is a box + All boxes are containers ⟹ Some containers are not bags (No+All rule) — definite (I). For II, the ‘containers that are baskets’ (statement 3) need not be the same containers proven not to be bags in step 1 — two ‘Some’-type facts about a shared term (Containers) don’t combine to link Baskets and Bags. II is undetermined.

Q61. Statements: I. All pens are pencils. II. All pencils are erasers. III. Some erasers are markers. IV. No marker is a crayon.
Conclusions: I. Some pens are not crayons. II. Some erasers are not crayons. III. All pens are markers.
(A) Only I follows (B) Only II follows (C) Only I and II follow (D) Only II and III follow
Answer: (B) Only II follows
Explanation: All pens are pencils + All pencils are erasers ⟹ All pens are erasers. But the next link, All pens are erasers + Some erasers are markers, is an All+Some combination, which gives NO definite conclusion — the chain to Pens breaks here, so I and III fail. The separate sub-chain, Some erasers are markers + No marker is crayon (Some+No rule), validly gives Some erasers are not crayons (II). Only II follows.

Q62. Statements: I. Some teachers are writers. II. All writers are poets. III. All poets are philosophers.
Conclusions: I. Some teachers are philosophers. II. All writers are philosophers. III. Some poets are teachers.
(A) Only I and II follow (B) Only I and III follow (C) All three follow (D) None follow
Answer: (C) All three follow
Explanation: Some teachers are writers + All writers are poets ⟹ Some teachers are poets (Some+All). This combined with All poets are philosophers ⟹ Some teachers are philosophers (I, chained Some+All rule again). Separately, All writers are poets + All poets are philosophers ⟹ All writers are philosophers (II). And ‘Some teachers are poets’ converts validly to ‘Some poets are teachers’ (III). All three follow.

Q63. Statements: I. All rivers are water bodies. II. Some water bodies are lakes. III. No lake is a pond.
Conclusions: I. Some rivers are not ponds. II. No lake is a pond. III. Some lakes are not ponds.
(A) Only II and III follow (B) Only I follows (C) All three follow (D) None follow
Answer: (A) Only II and III follow
Explanation: All rivers are water bodies + Some water bodies are lakes is an All+Some combination — NO definite river-lake link, so the chain to Ponds also fails for I. II is the given fact itself, definite. III follows from II by subalternation (a universal negative always yields the matching particular negative). Only II and III follow.

Q64. Statements: I. No apple is a banana. II. All bananas are fruits. III. Some fruits are vegetables.
Conclusions: I. Some fruits are not apples. II. Some vegetables are not apples. III. Some fruits are vegetables.
(A) Only I and III follow (B) Only II and III follow (C) All three follow (D) None follow
Answer: (A) Only I and III follow
Explanation: No apple is a banana + All bananas are fruits ⟹ Some fruits are not apples (No+All rule) — definite (I). For II, the ‘fruits that are vegetables’ (statement 3) need not be the same fruits proven not to be apples — two ‘Some’-type facts sharing the term Fruits don’t combine to link Vegetables and Apples, so II is undetermined. III is simply the given third statement, definite. Only I and III follow.

Q65. Statements: I. All soldiers are officers. II. All officers are men. III. All men are humans. IV. Some humans are mortal.
Conclusions: I. All soldiers are humans. II. Some soldiers are mortal. III. All officers are humans.
(A) Only I and III follow (B) Only I and II follow (C) All three follow (D) None follow
Answer: (A) Only I and III follow
Explanation: Chaining the first three All-statements validly gives All soldiers are humans (I) and All officers are humans (III). But the final step, All soldiers are humans + Some humans are mortal, is an All+Some combination, which gives NO definite conclusion about soldiers and mortality — a very common pitfall, since students often wrongly assume this chains through. II does not follow. Only I and III follow.

Q66. Statements: I. Some students are athletes. II. All athletes are fit people. III. All fit people are healthy.
Conclusions: I. Some students are healthy. II. All athletes are healthy.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Some students are athletes + All athletes are fit people ⟹ Some students are fit people (Some+All). This combined with All fit people are healthy ⟹ Some students are healthy (I) — a Some+All chain stays valid however many All-links follow it. Separately, All athletes are fit + All fit are healthy ⟹ All athletes are healthy (II). Both follow. (Contrast this with the previous question — a chain starting with ‘Some’ survives later ‘All’ links, but a chain ending in ‘Some’ after ‘All’ links does not.)

13. Coded (Symbolic) Syllogism

In coded syllogism, the four statement types (All / No / Some / Some-not) are replaced by symbols or letters, and a "key" is given (or must be inferred) telling you what each symbol means. The logic is IDENTICAL to ordinary syllogism — the only extra step is decoding.

How to Handle Coded Questions

Step 1 — Write down the code key clearly before doing anything else (e.g. @ = All, © = No, % = Some, $ = Some ... not).
Step 2 — Decode every statement into plain English (or just the A/E/I/O letters) on your rough sheet.
Step 3 — Apply the exact same rule table, conversion, subalternation and either-or checks from Chapters 2–4.
Step 4 — Decode the given conclusions the same way before matching them to your derived result.

The Code Key Used in This Chapter

Symbol	Meaning	Standard Type
A @ B	All A are B	A (Universal Affirmative)
A © B	No A is B	E (Universal Negative)
A % B	Some A are B	I (Particular Affirmative)
A $ B	Some A are not B	O (Particular Negative)

Warning:

Real exams change the code key in every single question — never assume '@' always means 'All' outside of this chapter. Always re-read the key given in that specific question before decoding.

14. Practice Questions — Coded Syllogism

Q67. Statements: I. A @ B II. B © C
Conclusions: I. A © C II. A $ C
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Decode: All A are B; No B is C. Rule table All+No=No: No A is C (I), definite. By subalternation, Some A are not C (II) also follows. Both follow.

Q68. Statements: I. P % Q II. Q @ R
Conclusions: I. P % R II. R % P
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Explanation: Decode: Some P are Q; All Q are R. Rule table Some+All=Some: Some P are R (I), definite. Its valid converse, Some R are P (II), also follows. Both follow.

Q69. Statements: I. X © Y II. Y % Z
Conclusions: I. Z $ X II. X © Z
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Decode: No X is Y; Some Y are Z. Rule table No+Some=Some(pred) are not (subj): Some Z are not X (I), definite. II is too strong to be guaranteed.

Q70. Statements: I. M @ N II. N % O
Conclusions: I. M % O II. M © O
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Decode: All M are N; Some N are O. Rule table All+Some=No definite conclusion — the M–O relation is completely open. I and II are the exact Some/No complementary pair, so Either I or II follows.

Q71. Statements: I. D $ E II. E © F
Conclusions: I. D $ F II. F % D
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (D) Neither I nor II follows
Explanation: Decode: Some D are not E; No E is F. Rule table Some-not+No=No definite conclusion for D and F. I and II are also stated in different directions (D→F vs F→D) and are not a valid contradictory pair. Neither follows.

Q72. Statements: I. A % B II. B @ C III. C © D
Conclusions: I. A $ D II. C © D III. A % C
(A) Only I and III follow (B) All three follow (C) Only II follows (D) None follow
Answer: (B) All three follow
Explanation: Step 1 (A%B + B@C, Some+All): Some A are C (III), definite. Step 2 (A%C + C©D, Some+No): Some A are not D (I), definite. II is simply the given third statement. All three follow.

Q73. Statements: I. All P @ Q II. All Q @ R III. Some R $ S
Conclusions: I. P $ S II. All P @ R III. Some R are not S
(A) Only I and II follow (B) Only II and III follow (C) All three follow (D) None follow
Answer: (B) Only II and III follow
Explanation: All P are Q + All Q are R ⟹ All P are R (II), definite. Combining All P are R with Some R are not S is an All+Some-not combination, which gives NO definite conclusion about P and S — I fails, a common pitfall. III is simply the given third statement, definite. Only II and III follow.

Q74. Statements: I. No A © B II. No B © C
Conclusions: I. No A is C. II. Some A are C.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Decode: No A is B; No B is C. Rule table No+No=No definite conclusion — chaining two negatives never fixes the relation between the extreme terms. I and II form the exact No/Some complementary pair, so Either I or II follows.

Q75. Statements: I. Some X % Y II. All Y @ Z III. No Z © W
Conclusions: I. Some X are not W. II. No Z is W. III. All Y are Z.
(A) Only I follows (B) Only I and II follow (C) All three follow (D) None follow
Answer: (C) All three follow
Explanation: Step 1 (X%Y + Y@Z, Some+All): Some X are Z, definite. Step 2 (X%Z + Z©W, Some+No): Some X are not W (I), definite. II and III simply restate the given second and third statements. All three follow.

Q76. Statements: I. All M @ N II. Some N % O III. No O © P
Conclusions: I. Some M are not P. II. Some N are not P. III. All M @ N (given).
(A) Only I and II follow (B) Only II and III follow (C) All three follow (D) None follow
Answer: (B) Only II and III follow
Explanation: All M are N + Some N are O is an All+Some combination — NO definite M–O link, so the chain to P also fails for I. The separate sub-chain, Some N are O + No O is P (Some+No), validly gives Some N are not P (II). III is the given first statement, definite. Only II and III follow.

15. The Standard Exam Format — Statement & Numbered Conclusions

Almost every SSC/RRB syllogism question is presented as one or more statements followed by numbered conclusions (I, II, sometimes III), with answer choices built from combinations of those numbers. Recognising the exact option pattern quickly saves time.

Common Two-Conclusion Option Patterns

Pattern	When it is used
Only I follows / Only II follows / Both follow / Neither follows	When "both true together" is logically possible (no contradiction between I and II).
Only I follows / Only II follows / Either I or II follows / Neither follows	When I and II are an approved complementary pair (Chapter 4) — "both together" is impossible, so "both follow" is replaced by "either...or".

Common Three-Conclusion Option Patterns

Only I follows / Only II follows / Only III follows / None follow
Only I and II follow / Only II and III follow / All three follow / None follow
Only I follows / I and either II or III follow / All follow / None follow — this rarer, more advanced pattern combines a definite conclusion with an either-or pair (see the capstone question in Chapter 10).

Method

1. Solve the statements independently first (rule table, chaining, either-or check) — decide what actually follows BEFORE reading the four answer options, so the options cannot bias your logic.
2. Match your derived result to the exact option that describes it.
3. Watch for options that restate a GIVEN premise as if it were a conclusion — some question-setters do treat a directly restated premise as "following", others do not; when uncertain, prioritise whichever conclusion is a genuine NEW inference.

16. Practice Questions — Standard Format Practice

Q77. Statements: I. All benches are seats. II. Some seats are wooden.
Conclusions: I. Some benches are wooden. II. All seats are wooden. III. Some seats are benches.
(A) Only III follows (B) Only I follows (C) Only I and III follow (D) None follow
Answer: (A) Only III follows
Explanation: Bench–wooden relation is undetermined (All+Some rule), so I fails; II is far too strong. But the first statement’s valid converse, Some seats are benches, always follows from ‘All benches are seats’. Only III follows.

Q78. Statements: I. No pillows are blankets. II. All blankets are fabrics.
Conclusions: I. Some fabrics are not pillows. II. All fabrics are blankets. III. No pillow is a fabric.
(A) Only I follows (B) Only II follows (C) Only I and III follow (D) All follow
Answer: (A) Only I follows
Explanation: Rule table No+All=Some(pred) not (subj): Some fabrics are not pillows (I), definite. II reverses the given relation and is unwarranted. III is too strong — pillows could still overlap fabrics through non-blanket fabrics.

Q79. Statements: I. Some windows are doors. II. All doors are wooden items.
Conclusions: I. Some windows are wooden items. II. Some wooden items are windows. III. All windows are wooden items.
(A) Only I and II follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and II follow
Explanation: Rule table Some+All=Some: Some windows are wooden items (I), definite; its valid converse, Some wooden items are windows (II), also follows. III is too strong.

Q80. Statements: I. All cups are ceramics. II. All ceramics are fragile items.
Conclusions: I. All cups are fragile items. II. Some fragile items are cups. III. No cup is a fragile item.
(A) Only I and II follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and II follow
Explanation: Rule table All+All=All: All cups are fragile items (I), definite; its valid converse, Some fragile items are cups (II), follows. III directly contradicts I.

Q81. Statements: I. Some laptops are tablets. II. No tablet is a typewriter.
Conclusions: I. Some laptops are not typewriters. II. No laptop is a typewriter. III. All laptops are typewriters.
(A) Only I follows (B) Only II follows (C) Only I and III follow (D) All follow
Answer: (A) Only I follows
Explanation: Rule table Some+No=Some(subj) not (pred): Some laptops are not typewriters (I), definite. II is too strong; III directly contradicts I and is impossible.

Q82. Statements: I. Some actors are dancers. II. Some dancers are singers.
Conclusions: I. Some actors are singers. II. No actor is a singer.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table Some+Some=No definite conclusion — the actor–singer relation is fully open. I and II form the exact Some/No complementary pair, so Either I or II follows (note: a third possible conclusion, ‘All dancers are singers’, does not follow either, since only ‘some’ dancers were stated to be singers).

Q83. Statements: I. No rings are bangles. II. Some bangles are ornaments.
Conclusions: I. Some ornaments are not rings. II. No ornament is a ring. III. Some rings are ornaments.
(A) Only I follows (B) Only II follows (C) Only I and III follow (D) All follow
Answer: (A) Only I follows
Explanation: Rule table No+Some=Some(pred) not (subj): Some ornaments are not rings (I), definite. II is too strong. III is undetermined — rings need not overlap ornaments at all.

Q84. Statements: I. All watches are gadgets. II. No gadget is furniture.
Conclusions: I. No watch is furniture. II. Some watches are not furniture. III. Some furniture is not a gadget.
(A) All three follow (B) Only I and II follow (C) Only I follows (D) None follow
Answer: (A) All three follow
Explanation: Rule table All+No=No: No watch is furniture (I), definite; by subalternation, Some watches are not furniture (II) also follows. Separately, ‘No gadget is furniture’ converts validly to ‘No furniture is a gadget’, which by subalternation gives Some furniture is not a gadget (III). All three follow.

Q85. Statements: I. Some notebooks are diaries. II. All diaries are stationery items.
Conclusions: I. Some notebooks are stationery items. II. All notebooks are stationery items. III. Some stationery items are diaries.
(A) Only I and III follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and III follow
Explanation: Rule table Some+All=Some: Some notebooks are stationery items (I), definite. II is too strong. Separately, the second statement’s valid converse gives Some stationery items are diaries (III).

Q86. Statements: I. No spoons are forks. II. All forks are utensils.
Conclusions: I. Some utensils are not spoons. II. Some utensils are forks. III. No spoon is a utensil.
(A) Only I and II follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and II follow
Explanation: Rule table No+All=Some(pred) not (subj): Some utensils are not spoons (I), definite. The second statement’s valid converse gives Some utensils are forks (II). III is too strong — spoons could still be utensils of a different kind.

17. Common Traps Examiners Use

Question-setters deliberately design wrong options around a small set of recurring mistakes. Knowing them by name lets you spot and reject the trap option almost instantly.

Trap	What goes wrong
Illicit conversion of O	Wrongly reversing "Some A are not B" into "Some B are not A" — O-type statements have NO valid converse.
Illicit conversion of A	Wrongly reversing "All A are B" into "All B are A" — only the weaker "Some B are A" is valid.
"Some" treated as "not all"	"Some" means "at least one"; it does not imply the rest are excluded.
No–No chain assumed transitive	Two negative statements chained together give NO definite relation between the extreme terms.
All–Some chain assumed transitive	"All A are B" + "Some B are C" gives NO definite conclusion — only "Some A are B" + "All B are C" (the reverse order) is valid.
Common-superset / common-subset pitfall	Two statements that share a term only as PREDICATE (or only as SUBJECT) in both give no relation between the other two terms.
Treating a possibility as a certainty	Marking a merely-possible conclusion as "follows" when the rule table gives no definite result.
Over-applying either-or	Applying the either-or shortcut to a Some/Some-not pair, which is never an approved complementary pair.
Reversed direction in either-or	Checking two conclusions written in OPPOSITE subject-predicate order as if they were a valid complementary pair.
Ignoring subalternation	Missing a second valid conclusion that follows automatically from an already-proven All/No statement.

18. Practice Questions — Spot the Trap

Q87. Statements: Some birds are not flyers.
Conclusions: Which of the following is a valid inference?
(A) Some flyers are not birds (B) All flyers are birds (C) No conclusion can be drawn about flyers (D) No bird is a flyer
Answer: (C) No conclusion can be drawn about flyers
Explanation: TRAP: illicit conversion of an O-type statement. ‘Some A are not B’ has NO valid converse — concluding ‘Some flyers are not birds’ is a very common but invalid move. No relationship between flyers and birds can be drawn from this alone.

Q88. Statements: Some engineers are managers.
Conclusions: Which is definitely true?
(A) All engineers are not managers (B) Not all engineers are managers (C) At least one engineer is a manager (D) No engineer is a manager
Answer: (C) At least one engineer is a manager
Explanation: TRAP: treating ‘some’ as meaning ‘not all’. In logic, ‘some’ only means ‘at least one’ — it does not imply that the rest are excluded. Option (B) is the classic wrong pick; the safe, definite reading is (C).

Q89. Statements: All squares are rectangles.
Conclusions: Which conclusion is actually valid, and which is the common wrong pick?
(A) All rectangles are squares (B) No rectangle is a square (C) Some rectangles are squares (D) Some rectangles are not squares
Answer: (C) Some rectangles are squares
Explanation: TRAP: illicit conversion of an A-type statement — students often wrongly pick ‘All rectangles are squares’, assuming a universal statement reverses completely. The only valid inference is the I-type converse: Some rectangles are squares.

Q90. Statements: I. No cats are dogs. II. No dogs are cows.
Conclusions: I. No cat is a cow. II. Some cats are not cows.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: TRAP: assuming a No–No chain transfers to the extreme terms. Rule table No+No=No definite conclusion — Cats and Cows could be the same set, overlapping sets, or fully separate, all while satisfying both premises. Neither conclusion is guaranteed.

Q91. Statements: I. All fans are electronics. II. Some electronics are expensive.
Conclusions: I. Some fans are expensive. II. Some fans are not expensive.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: TRAP: confusing this with the valid ‘Some+All’ pattern. Here the order is reversed — All+Some — which the rule table marks as NO definite conclusion. The expensive electronics need not include any fans at all. Neither follows.

Q92. Statements: No teachers are clerks.
Conclusions: Which is a valid conclusion?
(A) No clerk is a teacher (B) Some clerks are teachers (C) All clerks are teachers (D) Nothing can be said about clerks and teachers
Answer: (A) No clerk is a teacher
Explanation: Clarifying negative-statement confusion: unlike O-type statements, an E-type statement (‘No A is B’) DOES convert simply and validly to ‘No B is A’. The trap is assuming negative statements can never be converted at all — only O-type statements have that restriction.

Q93. Statements: I. Some fruits are sweet. II. All sweet things are enjoyable.
Conclusions: I. Some enjoyable things are fruits. II. Some enjoyable things are not fruits.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table Some+All=Some: Some fruits are enjoyable, definite; its valid converse gives I. TRAP: II wrongly flips the affirmative conclusion into a negative one that was never implied — this reversing-of-‘some’ error is very common.

Q94. Statements: I. Some pens are red. II. Some red things are costly.
Conclusions: I. Some pens are costly. II. Some pens are not costly.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: TRAP: treating a merely possible conclusion as definite. Rule table Some+Some=No definite conclusion — the red things that are costly need not be the same red things that are pens. Both I and II are only possibilities, not certainties.

Q95. Statements: I. All lions are carnivores. II. All tigers are carnivores.
Conclusions: I. Some lions are tigers. II. All tigers are lions.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Explanation: TRAP: the ‘common superset’ pitfall — both Lions and Tigers are merely subsets of Carnivores (Carnivores is the PREDICATE in both statements), which says nothing about how Lions and Tigers relate to each other. Neither follows.

Q96. Statements: I. Some actors are directors. II. Some directors are writers.
Conclusions: I. Some actors are writers. II. Some actors are not writers.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (D) Neither I nor II follows
Explanation: TRAP: wrongly applying the either-or rule to a Some/Some-not pair. Only the All/Some-not and No/Some pairs qualify for the either-or test — a Some/Some-not pair never does, by exam convention. Separately, rule table Some+Some=No definite conclusion, so neither follows individually either.

19. Step-by-Step Solving Framework for Exam Speed

Use this fixed checklist on every syllogism question, in order, without skipping steps — with practice this entire sequence takes well under 30 seconds.

1. Read both/all statements once and identify the TYPE (A/E/I/O) of each.
2. Identify the common (middle) term and check it is properly placed — predicate of one statement, subject of the next. If not (common-superset/subset pitfall), the extreme terms have no forced relation.
3. Apply the rule table to get the base conclusion (if any) about the extreme terms.
4. If more than two statements are given, chain step 3 forward one link at a time, watching especially for an All-then-Some break in the chain.
5. For every All/No conclusion found, also write down its subalternation partner (Some/Some-not) as a second valid conclusion.
6. For every All/Some conclusion found, also write down its valid converse as a possible second conclusion.
7. If the rule table gives "no definite conclusion", check the offered conclusions against the two approved either-or pairs before rejecting both.
8. Only now read the four answer options, and match your derived result to the exact wording.
9. Sanity-check: does any option contradict something you have already proven true? If so, it is impossible — eliminate it immediately.

Final Speed Tip:

Practice this checklist until it becomes automatic. In the actual exam you should never need to draw a full Venn diagram for a standard two-statement question — the rule table plus conversion/subalternation plus the either-or check covers well over 95% of questions asked.

20. Practice Questions — Mixed Review (Full Framework)

Q97. Statements: I. All coins are metals. II. Some metals are valuable.
Conclusions: I. Some coins are valuable. II. No coin is valuable.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Rule table All+Some=No definite conclusion. I/II form the exact Some/No complementary pair, so Either I or II follows.

Q98. Statements: I. No chairs are cushions. II. All cushions are soft items.
Conclusions: I. Some soft items are not chairs. II. All soft items are cushions.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table No+All=Some(pred) not (subj): Some soft items are not chairs (I), definite. II reverses the given relation and is unwarranted.

Q99. Statements: I. Some doctors are surgeons. II. All surgeons are specialists. III. No specialist is a novice.
Conclusions: I. Some doctors are not novices. II. No specialist is a novice. III. Some doctors are specialists.
(A) All three follow (B) Only I and II follow (C) Only III follows (D) None follow
Answer: (A) All three follow
Explanation: Some doctors are surgeons + All surgeons are specialists ⟹ Some doctors are specialists (III, Some+All). This combined with No specialist is a novice ⟹ Some doctors are not novices (I, Some+No). II is the given fact. All three follow.

Q100. Statements: I. F % G II. G $ H
Conclusions: I. F @ H II. F $ H
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither I nor II follows
Answer: (C) Either I or II follows
Explanation: Decode: Some F are G; Some G are not H. Rule table Some+Some-not=No definite conclusion for F and H — the relation is fully open. I and II form the exact All/Some-not complementary pair, so Either I or II follows.

Q101. Statements: I. All pillars are supports. II. All supports are structures.
Conclusions: I. All pillars are structures. II. Some structures are pillars. III. No pillar is a structure.
(A) Only I and II follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and II follow
Explanation: Rule table All+All=All: All pillars are structures (I), definite; its valid converse, Some structures are pillars (II), follows. III directly contradicts I.

Q102. Statements: I. Some rooms are halls. II. No hall is a corridor.
Conclusions: I. Some rooms are not corridors. II. All rooms are corridors.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table Some+No=Some(subj) not (pred): Some rooms are not corridors (I), definite. II directly contradicts I and is therefore impossible — not an either-or case.

Q103. Statements: I. All buses are vehicles. II. All vehicles are machines. III. Some machines are electric.
Conclusions: I. All buses are machines. II. Some buses are electric. III. Some machines are electric.
(A) Only I and III follow (B) Only I and II follow (C) All follow (D) None follow
Answer: (A) Only I and III follow
Explanation: All buses are vehicles + All vehicles are machines ⟹ All buses are machines (I), definite. But combining this with ‘Some machines are electric’ is an All+Some step, giving NO definite conclusion about buses and electric items — II is a common pitfall and does not follow. III is the given fact. Only I and III follow.

Q104. Statements: I. No windows are doors. II. All doors are exits.
Conclusions: I. Some exits are not windows. II. All exits are windows.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Explanation: Rule table No+All=Some(pred) not (subj): Some exits are not windows (I), definite. II directly contradicts I and is impossible — not an either-or case.

Q105. Statements: I. Some pencils are pens. II. All pens are ink-items. III. Some ink-items are not markers.
Conclusions: I. Some pencils are ink-items. II. All pencils are markers. III. Some pencils are not markers.
(A) I follows, and either II or III follows (B) Only I follows (C) All follow (D) None follow
Answer: (A) I follows, and either II or III follows
Explanation: Some pencils are pens + All pens are ink-items ⟹ Some pencils are ink-items (I), definite (Some+All). Whether this extends to ALL pencils being markers or SOME pencils are not markers is left completely open by the remaining premise — II and III form the exact All/Some-not complementary pair. I follows, and Either II or III follows.

Q106. Statements: I. All rivers are streams. II. No stream is stagnant.
Conclusions: I. No river is stagnant. II. Some rivers are not stagnant. III. Some stagnant things are streams.
(A) Only I and II follow (B) Only I follows (C) All follow (D) None follow
Answer: (A) Only I and II follow
Explanation: Rule table All+No=No: No river is stagnant (I), definite; by subalternation, Some rivers are not stagnant (II) follows. The second statement’s valid converse is ‘No stagnant thing is a stream’, which directly contradicts III — so III is actually false, not merely unproven.

21. Final Practice Set — 25 Mixed Questions

Attempt all 25 questions under timed conditions (aim for 12-15 minutes total) before checking the consolidated answer key that follows. This set mixes every technique covered in the book: the rule table, chaining, either-or, coded logic and common traps.

Q107. Statements: I. All lamps are bulbs. II. All bulbs are electric items.
Conclusions: I. All lamps are electric items. II. Some electric items are lamps.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Reason: All+All=All gives I; its valid converse gives II.

Q108. Statements: I. No pens are erasers. II. Some erasers are stationery.
Conclusions: I. Some stationery items are not pens. II. No pen is a stationery item.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: No+Some=Some(pred) not(subj) gives I; II is too strong.

Q109. Statements: I. Some actors are singers. II. All singers are celebrities.
Conclusions: I. Some actors are celebrities. II. All actors are celebrities.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: Some+All=Some gives I; II is too strong.

Q110. Statements: I. All keys are metals. II. Some metals are heavy.
Conclusions: I. Some keys are heavy. II. No key is heavy.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither follows
Answer: (C) Either I or II follows
Reason: All+Some=No definite link; I/II are the exact Some/No complementary pair.

Q111. Statements: I. Some boxes are cartons. II. Some cartons are fragile.
Conclusions: I. Some boxes are fragile. II. Some boxes are not fragile.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Reason: Some+Some=No definite conclusion; Some/Some-not is not an approved either-or pair.

Q112. Statements: I. No cups are plates. II. All plates are ceramic.
Conclusions: I. Some ceramic items are not cups. II. All ceramic items are plates.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: No+All=Some(pred) not(subj) gives I; II reverses the given relation.

Q113. Statements: I. All windows are glass. II. No glass is metal.
Conclusions: I. No window is metal. II. Some windows are not metal.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Reason: All+No=No gives I directly; subalternation gives II.

Q114. Statements: I. Some doctors are teachers. II. No teacher is a clerk.
Conclusions: I. Some doctors are not clerks. II. All doctors are clerks.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: Some+No=Some(subj) not(pred) gives I; II directly contradicts I, so it is impossible.

Q115. Statements: I. All actors are artists. II. All artists are famous. III. Some famous people are rich.
Conclusions: I. All actors are famous. II. Some actors are rich. III. Some famous people are rich.
(A) Only I and III follow (B) Only I and II follow (C) All follow (D) None follow
Answer: (A) Only I and III follow
Reason: All+All gives I; the final All+Some step breaks the chain to actors-rich (II fails); III is the given fact.

Q116. Statements: I. No students are lazy. II. Some lazy people are poor.
Conclusions: I. Some poor people are not students. II. No poor person is a student.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: No+Some=Some(pred) not(subj) gives I; II is too strong.

Q117. Statements: I. F @ G II. G % H
Conclusions: I. F % H II. F © H
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither follows
Answer: (C) Either I or II follows
Reason: All+Some=No definite link; I/II are the exact Some/No complementary pair.

Q118. Statements: I. Some pilots are engineers. II. All engineers are graduates. III. No graduate is uneducated.
Conclusions: I. Some pilots are not uneducated. II. No graduate is uneducated. III. Some pilots are graduates.
(A) All three follow (B) Only I and II follow (C) Only III follows (D) None follow
Answer: (A) All three follow
Reason: Some+All gives III; III combined with the No statement (Some+No) gives I; II is the given fact.

Q119. Statements: I. All actors are dancers. II. All singers are dancers.
Conclusions: I. Some actors are singers. II. All singers are actors.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Reason: Common-superset pitfall: Dancers is the predicate in both statements, so Actors and Singers have no forced relationship.

Q120. Statements: I. Some keys are broken. II. All broken things are useless.
Conclusions: I. Some keys are useless. II. Some useless things are keys.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Reason: Some+All=Some gives I; its valid converse gives II.

Q121. Statements: I. No trains are buses. II. Some buses are vehicles.
Conclusions: I. Some vehicles are not trains. II. All vehicles are buses.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: No+Some=Some(pred) not(subj) gives I; II is far too strong.

Q122. Statements: I. Some mangoes are yellow. II. Some yellow things are sweet.
Conclusions: I. Some mangoes are sweet. II. All mangoes are sweet.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Reason: Some+Some=No definite conclusion; I is only possible, II is far too strong.

Q123. Statements: I. P @ Q II. Some Q $ R
Conclusions: I. All P are R. II. Some P are not R.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither follows
Answer: (C) Either I or II follows
Reason: All+Some-not=No definite link for P and R; I/II are the exact All/Some-not complementary pair.

Q124. Statements: I. Some books are novels. II. No novel is a magazine.
Conclusions: I. Some books are not magazines. II. All books are magazines.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: Some+No=Some(subj) not(pred) gives I; II directly contradicts I, so it is impossible.

Q125. Statements: I. All buses are vehicles. II. Some vehicles are old. III. No old thing is valuable.
Conclusions: I. Some buses are not valuable. II. Some vehicles are not valuable. III. All buses are vehicles.
(A) Only II and III follow (B) Only I and II follow (C) All follow (D) None follow
Answer: (A) Only II and III follow
Reason: All+Some breaks the bus–old link, so I fails; the separate sub-chain Some+No gives II; III is the given fact.

Q126. Statements: I. Some actors are not singers. II. All singers are performers.
Conclusions: I. Some actors are performers. II. Some actors are not performers.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (D) Neither follows
Reason: Some-not+All=No definite conclusion — a classic trap where the excluded actors have no fixed relation to performers.

Q127. Statements: I. No pens are broken. II. All broken things are discarded.
Conclusions: I. Some discarded things are not pens. II. No discarded thing is a pen.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (A) Only I follows
Reason: No+All=Some(pred) not(subj) gives I; II is too strong.

Q128. Statements: I. Some flowers are red. II. All red things are colourful. III. Some colourful things are expensive.
Conclusions: I. Some flowers are expensive. II. Some flowers are colourful. III. All red things are colourful.
(A) Only II and III follow (B) Only I and II follow (C) All follow (D) None follow
Answer: (A) Only II and III follow
Reason: Some+All gives II; the next step (Some+Some) breaks the chain to expensive items, so I fails; III is the given fact.

Q129. Statements: I. X @ Y II. No Y © Z
Conclusions: I. No X is Z. II. Some X are not Z.
(A) Only I follows (B) Only II follows (C) Both follow (D) Neither follows
Answer: (C) Both follow
Reason: All+No=No gives I directly; subalternation gives II.

Q130. Statements: I. Some pens are not blue. II. Some blue things are costly.
Conclusions: I. Some pens are costly. II. No pen is costly.
(A) Only I follows (B) Only II follows (C) Either I or II follows (D) Neither follows
Answer: (C) Either I or II follows
Reason: Some-not+Some=No definite link; I/II are the exact Some/No complementary pair.

Q131. Statements: I. Some pens are markers. II. All markers are stationery. III. No stationery is furniture.
Conclusions: I. Some pens are not furniture. II. No stationery is furniture. III. Some pens are stationery.
(A) All three follow (B) Only I and II follow (C) Only III follows (D) None follow
Answer: (A) All three follow
Reason: Some+All gives III; III combined with the No statement (Some+No) gives I; II is the given fact.

22. Consolidated Answer Key — Final Practice Set

Q.No	Answer	Brief Reasoning
107	(C) Both follow	All+All=All gives I; its valid converse gives II.
108	(A) Only I follows	No+Some=Some(pred) not(subj) gives I; II is too strong.
109	(A) Only I follows	Some+All=Some gives I; II is too strong.
110	(C) Either I or II follows	All+Some=No definite link; I/II are the exact Some/No complementary pair.
111	(D) Neither follows	Some+Some=No definite conclusion; Some/Some-not is not an approved either-or pair.
112	(A) Only I follows	No+All=Some(pred) not(subj) gives I; II reverses the given relation.
113	(C) Both follow	All+No=No gives I directly; subalternation gives II.
114	(A) Only I follows	Some+No=Some(subj) not(pred) gives I; II directly contradicts I, so it is impossible.
115	(A) Only I and III follow	All+All gives I; the final All+Some step breaks the chain to actors-rich (II fails); III is the given fact.
116	(A) Only I follows	No+Some=Some(pred) not(subj) gives I; II is too strong.
117	(C) Either I or II follows	All+Some=No definite link; I/II are the exact Some/No complementary pair.
118	(A) All three follow	Some+All gives III; III combined with the No statement (Some+No) gives I; II is the given fact.
119	(D) Neither follows	Common-superset pitfall: Dancers is the predicate in both statements, so Actors and Singers have no forced relationship.
120	(C) Both follow	Some+All=Some gives I; its valid converse gives II.
121	(A) Only I follows	No+Some=Some(pred) not(subj) gives I; II is far too strong.
122	(D) Neither follows	Some+Some=No definite conclusion; I is only possible, II is far too strong.
123	(C) Either I or II follows	All+Some-not=No definite link for P and R; I/II are the exact All/Some-not complementary pair.
124	(A) Only I follows	Some+No=Some(subj) not(pred) gives I; II directly contradicts I, so it is impossible.
125	(A) Only II and III follow	All+Some breaks the bus–old link, so I fails; the separate sub-chain Some+No gives II; III is the given fact.
126	(D) Neither follows	Some-not+All=No definite conclusion — a classic trap where the excluded actors have no fixed relation to performers.
127	(A) Only I follows	No+All=Some(pred) not(subj) gives I; II is too strong.
128	(A) Only II and III follow	Some+All gives II; the next step (Some+Some) breaks the chain to expensive items, so I fails; III is the given fact.
129	(C) Both follow	All+No=No gives I directly; subalternation gives II.
130	(C) Either I or II follows	Some-not+Some=No definite link; I/II are the exact Some/No complementary pair.
131	(A) All three follow	Some+All gives III; III combined with the No statement (Some+No) gives I; II is the given fact.

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TOC Index

Table of Contents

1. Introduction to Syllogism

What Syllogism Tests

Why It Is High-Weightage

The Four Categorical Statement Types

Immediate Inferences (Conversion) for Each Type

Subalternation (a second useful immediate inference)

2. Practice Questions — Statement Types & Conversion

3. The Venn Diagram Method

Drawing All Possible Diagrams

Worked Example

Definitely True vs Possibly True

4. Practice Questions — Venn Diagram Method

5. The Rules-Based (Shortcut) Method

The Master Rule Table

Using the Table — Step by Step

6. Practice Questions — Rules-Based Method

7. Complementary Pairs — Either-Or Conclusions

The Two Approved Complementary Pairs

The Exact Test to Apply

Worked Example

8. Practice Questions — Either-Or / Complementary Pairs

9. Possibility-Based Questions

The Three Categories

How Exam-Setters Phrase These Questions

Worked Example

10. Practice Questions — Possibility-Based

11. Three-Statement and Four-Statement Syllogisms

The Chaining Procedure

The Most Important Pitfall: Direction Sensitivity

The "Common Superset" Pitfall

12. Practice Questions — Three & Four Statement Syllogisms

13. Coded (Symbolic) Syllogism

How to Handle Coded Questions

The Code Key Used in This Chapter

14. Practice Questions — Coded Syllogism

15. The Standard Exam Format — Statement & Numbered Conclusions

Common Two-Conclusion Option Patterns

Common Three-Conclusion Option Patterns

Method

16. Practice Questions — Standard Format Practice

17. Common Traps Examiners Use

18. Practice Questions — Spot the Trap

19. Step-by-Step Solving Framework for Exam Speed

20. Practice Questions — Mixed Review (Full Framework)

21. Final Practice Set — 25 Mixed Questions

22. Consolidated Answer Key — Final Practice Set