In this guide
Syllogism questions ask you to accept a set of statements as true — even if they sound absurd, like "All cats are cars" — and decide which conclusions must follow. The only reliable method is to draw Venn diagrams that show every way the statements could be true, and accept a conclusion only if it holds in every diagram.
The four statement types
| Statement | Meaning | Diagram |
|---|---|---|
| All A are B | Circle A lies entirely inside circle B | A inside B |
| No A is B | Circles A and B don't touch | Separate circles |
| Some A are B | Circles A and B overlap (at least one A is B) | Overlapping circles |
| Some A are not B | At least part of A lies outside B | Part of A outside B |
Direct conclusions
- All A are B → Some A are B and Some B are A are true.
- Some A are B → Some B are A is true.
- No A is B → No B is A is true; Some A are not B is true.
- All A are B does not mean All B are A.
The method
- Draw the basic diagram that satisfies all the statements with the fewest overlaps.
- Check each conclusion against the basic diagram.
- If a conclusion fails in the basic diagram, it does not follow (for definite conclusions).
- For "possibility" conclusions, check whether you could draw a diagram in which it is true without breaking any statement.
Worked examples
Example 1
Statements: All pens are books. Some books are bags.
Conclusions: I. Some pens are bags. II. Some bags are books.
Basic diagram: the pens circle inside books; bags overlapping books but not necessarily touching pens.
- I does not follow — pens and bags may not overlap.
- II follows — from "some books are bags".
Answer: only II follows.
Example 2
Statements: No flower is a tree. All trees are plants.
Conclusions: I. No flower is a plant. II. Some plants are trees.
- I does not follow — flowers could overlap with the part of plants that isn't trees.
- II follows — all trees are plants, so some plants are trees.
Answer: only II follows.
Example 3 (possibility)
Statements: Some cars are buses. All buses are trucks.
Conclusions: I. Some cars are trucks. II. All trucks being cars is a possibility.
- I follows — the cars that are buses are also trucks.
- II: can we draw trucks entirely inside cars? We would need the buses (inside trucks) inside cars too — but only "some" cars are buses, which still allows it. The statements don't forbid it, so II follows as a possibility.
Answer: both follow.
Either–or cases
When two conclusions are about the same two groups and one of them must be true — such as "Some A are B" and "No A is B" — and neither follows on its own, the answer is either I or II follows.
Example 4
Statements: All roses are red. Some red things are cars.
Conclusions: I. Some roses are cars. II. No rose is a car.
Neither follows definitely, but together they cover every possibility (either some roses are cars or none are). Answer: either I or II follows.
Common traps
| Trap | Fix |
|---|---|
| Using real-world knowledge | Only the statements count |
| Reversing "All A are B" | All B are A does not follow |
| Treating "some" as "only some" | "Some" can mean all |
| Missing either–or pairs | Check complementary conclusions |
Practice
- Statements: All doctors are engineers. All engineers are teachers. Conclusions: I. All doctors are teachers. II. Some teachers are doctors.
- Statements: Some apples are mangoes. No mango is a grape. Conclusions: I. Some apples are not grapes. II. No apple is a grape.
- Statements: All chairs are tables. No table is a bed. Conclusions: I. No chair is a bed. II. Some beds are chairs.
- Statements: Some books are pens. Some pens are pencils. Conclusions: I. Some books are pencils. II. No book is a pencil.
Answers: 1. Both follow. 2. Only I follows. 3. Only I follows. 4. Either I or II follows.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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