Syllogism for IBPS Clerk

In a syllogism question you get two or three statements and two conclusions. You decide which conclusions must follow from the statements, ignoring what you know about the real world. If the question says "All cats are rivers", then in that question all cats are rivers.

Syllogism is one of the quick types in the prelims, so it is worth making fast and reliable. The good news is that the method is mechanical. Draw the smallest diagram the statements allow, then test each conclusion by trying to break it. A conclusion that cannot be broken follows. A conclusion that can be broken does not.

What each statement guarantees

Two conversions come up constantly:

• "All A are B" gives "Some B are A", but not "All B are A".
• "Some A are not B" cannot be converted at all. It says nothing about B.

The Venn method

1. Draw the minimum diagram. For each statement, draw only the overlap it guarantees. Do not add any overlap the statements do not force.
2. Test each conclusion against that diagram. If it is false there, it does not follow.
3. Try to break it. If it looks true, try moving the circles into any other position the statements still allow. If you can make it false, it does not follow. If you cannot, it follows.

This works because a conclusion must hold in every arrangement the statements allow. Finding one arrangement where it fails is enough to reject it.

Either–or pairs

Sometimes neither conclusion follows on its own, but between them they cover every possibility. Then the answer is "Either I or II follows". Three conditions must all hold:

• Both conclusions are about the same two terms.
• Neither follows on its own.
• They are a complementary pair: "Some A are B" with "No A is B", or "All A are B" with "Some A are not B".

Possibility conclusions

A conclusion like "All A being C is a possibility" asks a different question: can it be true in at least one arrangement the statements allow? You are no longer trying to break it; you are trying to build it.

• A possibility follows if you can draw one valid diagram in which it is true.
• It fails if the statements force the opposite. The usual reason is a "No" statement. If no B is C and all A are B, then A and C can never meet, so "Some A being C is a possibility" fails.

Worked examples

Example 1. Statements: All pens are books. All books are bags.
Conclusions: I. All pens are bags. II. Some bags are pens.

1. Pens sit inside books, and books inside bags, so pens sit inside bags. I follows.
2. All pens are bags, so some bags are pens. II follows.
3. Both follow.

Example 2. Statements: Some cats are dogs. No dog is a rat.
Conclusions: I. Some cats are not rats. II. No cat is a rat.

1. The cats that are dogs cannot be rats. So some cats are not rats. I follows.
2. Other cats, outside the dog circle, could be rats. II can be broken.
3. Only I follows.

Example 3. Statements: All apples are fruits. Some fruits are red.
Conclusions: I. Some apples are red. II. Some fruits are apples.

1. The red part of fruits can sit entirely outside apples. I can be broken.
2. All apples are fruits, so some fruits are apples. II follows.
3. Only II follows.

Example 4. Statements: Some A are B. No B is C.
Conclusions: I. Some A are C. II. No A is C.

1. The part of A outside B may or may not touch C. So neither conclusion is certain.
2. Both are about A and C, and "some" and "no" are complementary: one of them must be true.
3. Either I or II follows.

Example 5. Statements: No shirt is a tie. All ties are belts.
Conclusions: I. Some belts are not shirts. II. All shirts being belts is a possibility.

1. The ties are belts, and no tie is a shirt. So those belts are not shirts. I follows.
2. Draw the shirt circle inside the belt circle but away from ties. Every statement still holds. II follows.
3. Both follow.

Example 6. Statements: All kites are planes. No plane is a ship.
Conclusions: I. Some kites being ships is a possibility. II. All planes being kites is a possibility.

1. Kites are inside planes, and planes never touch ships. Kites can never be ships. I fails.
2. The kite circle can be the same size as the plane circle. All kites are planes still holds. II follows.
3. Only II follows.

Example 7 (three statements). Statements: Some A are B. All B are C. No C is D.
Conclusions: I. Some A are not D. II. Some C are A.

1. The A that are B are also C, and no C is D. So those A are not D. I follows.
2. The same A that are B are inside C. So some C are A. II follows.
3. Both follow.

Common mistakes

• Using real-world knowledge ("all roses are red" feels false, but in the question it is true).
• Converting "All A are B" into "All B are A".
• Treating "Some A are not B" as if it also said "Some B are not A".
• Marking "either–or" when one of the two conclusions already follows on its own.
• Rejecting a possibility conclusion because it is not certain. Possibility only needs one valid diagram.

Practice

Set a six-minute timer. For each, decide: only I, only II, either I or II, neither, or both.

1. Statements: All chairs are tables. No table is a lamp. Conclusions: I. No chair is a lamp. II. Some lamps are chairs.
2. Statements: Some books are pens. Some pens are pencils. Conclusions: I. Some books are pencils. II. No book is a pencil.
3. Statements: All roses are flowers. All flowers are plants. Conclusions: I. All roses are plants. II. All plants are roses.
4. Statements: Some coins are notes. All notes are cards. Conclusions: I. Some cards are coins. II. All coins being cards is a possibility.
5. Statements: No pen is a ruler. Some rulers are erasers. Conclusions: I. Some erasers are not pens. II. Some pens are erasers.
6. Statements: All boxes are bags. Some bags are tins. Conclusions: I. Some boxes are tins. II. Some boxes being tins is a possibility.
7. Statements: All doctors are teachers. Some teachers are singers. No singer is a dancer. Conclusions: I. Some teachers are not dancers. II. No doctor is a dancer.
8. Statements: All X are Y. No Y is Z. Conclusions: I. All Z being X is a possibility. II. No X is Z.

Answers:

1. Only I. Chairs are inside tables, which never touch lamps. So no lamp is a chair, and II is false.
2. Either I or II. Neither is certain, both are about books and pencils, and "some" and "no" cover every case.
3. Only I. Plants can include things that are not roses.
4. Both. The coins that are notes are cards, so some cards are coins. The coin circle can be drawn inside cards.
5. Only I. The erasers that are rulers are not pens. Pens and erasers may or may not overlap, so II can be broken.
6. Only II. Tins can sit outside boxes, so I can be broken. But the box circle can be drawn to touch tins, so II follows.
7. Only I. The teachers who are singers are not dancers. Doctors could be teachers who are dancers, so II can be broken.
8. Only II. X is inside Y, and Y never touches Z, so no X is Z. Z can never be inside X.

What to do next

• Draw the minimum diagram for every practice question, even when the answer seems obvious. The habit protects you on the hard ones.
• Do 15 syllogisms a day for a week, then mix in possibility questions.
• Practise alongside inequality in the quick-types block of the reasoning plan, and see inequality for the other half of that block.