Syllogisms
CSAT · Logical Reasoning
Introduction
Syllogism questions give two or more statements, assumed true even if they sound odd, and ask which conclusions must follow. The safest method is to draw Venn diagrams and look for any arrangement that breaks a conclusion.
Key concepts
The four statement types
| Type | Form | Venn picture |
|---|---|---|
| A (universal affirmative) | All X are Y | X circle inside Y |
| E (universal negative) | No X is Y | X and Y separate |
| I (particular affirmative) | Some X are Y | X and Y overlap (at least one common) |
| O (particular negative) | Some X are not Y | part of X lies outside Y |
Method: try to break the conclusion
- Draw the most basic diagram that satisfies all statements.
- For each conclusion, try to redraw the circles so that the statements still hold but the conclusion fails.
- If you can break it, it does not follow. If no diagram breaks it, it follows.
Rules that save time
- All + All = All (All A are B, all B are C → all A are C).
- All + No = No (All A are B, no B is C → no A is C).
- Some + All = Some (Some A are B, all B are C → some A are C).
- Some + No = Some not (Some A are B, no B is C → some A are not C).
- All + Some, Some + Some → no definite conclusion between the end terms.
- Conversion: 'Some A are B' ⇒ 'Some B are A'; 'All A are B' ⇒ 'Some B are A'; 'No A is B' ⇒ 'No B is A'. 'Some A are not B' cannot be converted.
Assume each category exists
UPSC-style questions treat every category as non-empty, so 'All A are B' also gives 'Some A are B'.
- A + A → A
- A + E → E
- I + A → I
- I + E → O (about the first term)
- A + I, I + I → no conclusion
Solved examples
Example 1
Statements: All ponds are lakes. No lakes are rivers.
Conclusions: I. Some ponds are not rivers. II. Some lakes are not rivers.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I holds in every diagram that fits the statements – it follows.
- Conclusion II holds in every diagram that fits the statements – it follows.
Answer: (c) Both I and II follow
Example 2
Statements: All doctors are teachers. Some teachers are singers.
Conclusions: I. All teachers are doctors. II. Some singers are teachers.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I does not follow – counter-diagram with groups: teachers and singers; doctors and teachers and singers.
- Conclusion II holds in every diagram that fits the statements – it follows.
Answer: (b) Only conclusion II follows
Example 3
Statements: All kites are clouds. All clouds are birds.
Conclusions: I. Some clouds are birds. II. Some birds are not clouds.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I holds in every diagram that fits the statements – it follows.
- Conclusion II does not follow – counter-diagram with groups: kites and clouds and birds.
Answer: (a) Only conclusion I follows
Example 4
Statements: All desks are chairs. All chairs are tables.
Conclusions: I. All chairs are desks. II. Some desks are not chairs.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I does not follow – counter-diagram with groups: chairs and tables; desks and chairs and tables.
- Conclusion II does not follow – counter-diagram with groups: desks and chairs and tables.
Answer: (d) Neither I nor II follows
Example 5
Statements: Some books are pens. No pens are bags.
Conclusions: I. No books are bags. II. No bags are books.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I does not follow – counter-diagram with groups: books and bags; books and pens.
- Conclusion II does not follow – counter-diagram with groups: books and bags; books and pens.
Answer: (d) Neither I nor II follows
Example 6
Statements: All plants are roses. All roses are flowers.
Conclusions: I. Some plants are not flowers. II. Some plants are roses.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I does not follow – counter-diagram with groups: plants and roses and flowers.
- Conclusion II holds in every diagram that fits the statements – it follows.
Answer: (b) Only conclusion II follows
Example 7
Statements: All pens are books. All books are bags.
Conclusions: I. No books are bags. II. No pens are books.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I does not follow – counter-diagram with groups: pens and books and bags.
- Conclusion II does not follow – counter-diagram with groups: pens and books and bags.
Answer: (d) Neither I nor II follows
Example 8
Statements: All roses are flowers. All flowers are plants.
Conclusions: I. Some flowers are roses. II. No flowers are plants.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
- Conclusion I holds in every diagram that fits the statements – it follows.
- Conclusion II does not follow – counter-diagram with groups: roses and flowers and plants.
Answer: (a) Only conclusion I follows
- A conclusion with 'all' is the easiest to break – look for one counter-diagram.
- Check whether a conclusion simply restates a statement after conversion.
- When two conclusions are 'Some A are B' and 'No A is B', they form a complementary pair – exactly one is true (this is the 'either–or' case).
- Using real-world knowledge – only the statements count.
- Converting 'All A are B' into 'All B are A'.
- Assuming 'Some A are B' means 'Some A are not B' as well.
Practice set
Attempt all 10 questions (about 90 seconds each), then check the worked solutions below.
Q1. Statements: Some trucks are buses. No buses are cars.
Conclusions: I. No trucks are cars. II. Some cars are not buses.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q2. Statements: All ponds are rivers. All rivers are lakes.
Conclusions: I. All ponds are lakes. II. Some ponds are not lakes.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q3. Statements: All books are pens. All pens are bags.
Conclusions: I. All pens are books. II. Some bags are books.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q4. Statements: Some writers are poets. All poets are artists.
Conclusions: I. Some poets are not writers. II. No writers are artists.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q5. Statements: No singers are doctors. Some doctors are teachers.
Conclusions: I. Some doctors are singers. II. No teachers are singers.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q6. Statements: All doctors are teachers. All teachers are singers.
Conclusions: I. All singers are teachers. II. No doctors are singers.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q7. Statements: All trees are hills. Some hills are rocks.
Conclusions: I. All rocks are hills. II. Some trees are not hills.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q8. Statements: All rivers are ponds. No ponds are lakes.
Conclusions: I. Some ponds are not rivers. II. No lakes are rivers.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q9. Statements: No plates are bowls. No bowls are cups.
Conclusions: I. All bowls are plates. II. Some plates are not cups.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q10. Statements: No notes are coins. All coins are cards.
Conclusions: I. All cards are notes. II. Some notes are not coins.
Which conclusion(s) follow?
(a) Only conclusion I follows (b) Only conclusion II follows (c) Both I and II follow (d) Neither I nor II follows
Q1 – (b) Only conclusion II follows. Conclusion I does not follow – counter-diagram with groups: trucks and cars; trucks and buses. Conclusion II holds in every diagram that fits the statements – it follows.
Q2 – (a) Only conclusion I follows. Conclusion I holds in every diagram that fits the statements – it follows. Conclusion II does not follow – counter-diagram with groups: ponds and rivers and lakes.
Q3 – (b) Only conclusion II follows. Conclusion I does not follow – counter-diagram with groups: pens and bags; books and pens and bags. Conclusion II holds in every diagram that fits the statements – it follows.
Q4 – (d) Neither I nor II follows. Conclusion I does not follow – counter-diagram with groups: writers and poets and artists. Conclusion II does not follow – counter-diagram with groups: writers and poets and artists.
Q5 – (d) Neither I nor II follows. Conclusion I does not follow – counter-diagram with groups: doctors and teachers; singers and teachers. Conclusion II does not follow – counter-diagram with groups: doctors and teachers; singers and teachers.
Q6 – (d) Neither I nor II follows. Conclusion I does not follow – counter-diagram with groups: singers only; doctors and teachers and singers. Conclusion II does not follow – counter-diagram with groups: doctors and teachers and singers.
Q7 – (d) Neither I nor II follows. Conclusion I does not follow – counter-diagram with groups: rocks only; trees and hills and rocks. Conclusion II does not follow – counter-diagram with groups: trees and hills and rocks.
Q8 – (b) Only conclusion II follows. Conclusion I does not follow – counter-diagram with groups: lakes only; rivers and ponds. Conclusion II holds in every diagram that fits the statements – it follows.
Q9 – (d) Neither I nor II follows. Conclusion I does not follow – counter-diagram with groups: bowls only; plates and cups. Conclusion II does not follow – counter-diagram with groups: bowls only; plates and cups.
Q10 – (b) Only conclusion II follows. Conclusion I does not follow – counter-diagram with groups: coins and cards; notes and cards. Conclusion II holds in every diagram that fits the statements – it follows.
- Draw, then try to break
- A+A=A, A+E=E, I+A=I, I+E=O
- Convert I and E freely; A → I only; never O
- Ignore real-world facts
