Syllogism — IBPS PO Reasoning
Syllogism gives you statements you must treat as absolutely true — even "All pens are mountains" — and conclusions to validate. The only legal question is: does this conclusion HAVE to be true in every diagram the statements allow? If you can draw even one valid diagram where it fails, it does not follow. That is the whole game: not logic-in-your-head, but drawing the minimal Venn diagram and testing against it. In IBPS these are 3–5 fast Prelims marks and a new-pattern Mains set — high accuracy, low time, once the method is automatic.
1. What IBPS actually asks
- Prelims: 3–5 standard syllogisms — 2–3 statements, 2 conclusions, "which follow?"
- Mains: the new-pattern variants — reverse syllogism (given conclusions, find the statements), coded syllogism (statements written with symbols), and possibility-heavy sets ("only a few", "does not follow only in one case").
The statements use four quantifiers, and each maps to a Venn relationship:
| Statement | Meaning | Diagram |
|---|---|---|
| All A are B | A lies entirely inside B | small A circle inside B |
| No A is B | A and B are separate | two non-touching circles |
| Some A are B | A and B overlap | two overlapping circles |
| Some A are not B | part of A is outside B | overlap with a bit of A outside |
2. The minimal-diagram method (this is the chapter)
- Draw the most restrictive diagram the statements force — nothing more. If it says "Some A are B", draw exactly one overlap; do not add extra containment you weren't told.
- Test each conclusion against that diagram. If it holds in every legal diagram, it follows. If you can redraw legally so it fails, it does not.
- "Definitely true" needs universality; "possibility" needs just one case. A "definitely follows" conclusion must survive all diagrams; a "possibility" (Case) conclusion only needs one valid diagram where it holds.
You are not deciding whether the conclusion is realistic — you are deciding whether it is forced. Treat every statement as gospel and let the diagram, not intuition, rule.
3. The rules that settle 90% of cases
- "Some" is symmetric and never becomes "all". "Some A are B" ⇒ "Some B are A", but never "All". IBPS's favourite trap is offering "All A are B" as a conclusion from a "some" statement.
- Two negatives give nothing. From "No A is B" + "No B is C" you cannot conclude anything definite about A and C.
- "All + All" chains. "All A are B" + "All B are C" ⇒ "All A are C" and "Some C are A".
- "All + No" gives "No". "All A are B" + "No B is C" ⇒ "No A is C" (and "Some C are not A").
- The either–or case. When two conclusions are individually uncertain but together cover all possibilities and are complementary (same subject–predicate, one positive one negative, e.g. "Some A are C" / "No A is C"), the answer is "either I or II follows". This is the single most-missed pattern — spot the complementary pair.
4. Possibility ("only a few", "some ... can be all")
Modern IBPS leans on possibility conclusions: "All A being C is a possibility." This follows if you can draw a legal diagram where all A sit inside C without violating any statement. Method: try to force the possibility; if no rule blocks it, it's valid.
The phrase "only a few A are B" means "some A are B" AND "some A are not B" — it explicitly denies "all". Treat it as a stronger "some".
5. Reverse & coded syllogism (Mains)
Reverse syllogism gives the conclusions and asks which statement set guarantees them. Method: take each option's statements, draw their minimal diagram, and check whether all the given conclusions are forced. The correct option is the one whose diagram makes every conclusion definitely true.
Coded syllogism replaces words with symbols ("A @ B means all A are B; A # B means no A is B…"). Decode first — rewrite every symbolic statement in plain "All/No/Some" form — then it is an ordinary syllogism. Never try to reason on the symbols directly.
Solved examples
Q1. Statements: All books are pens. Some pens are red. Conclusions: (I) Some books are red. (II) All pens are books.
Show explanation
Solution. Draw: books inside pens; red overlaps pens (but need not touch books). (I) "Some books are red" is not forced — red may sit in the pen-region outside books. (II) "All pens are books" contradicts "books inside pens". Neither follows.
Q2 (either–or). Statements: Some cats are dogs. No dog is a cow. Conclusions: (I) Some cats are cows. (II) No cat is a cow.
Show explanation
Solution. Cats overlap dogs; dogs separate from cows. Cats may extend into cows (I true) or may not (II true) — both are possible, they are complementary and exhaustive. Answer: either I or II follows.
Q3 (all + no). Statements: All pens are inks. No ink is red. Conclusion: No pen is red.
Show explanation
Solution. Pens inside inks; inks separate from red ⇒ pens are separate from red. Follows.
Q4 (possibility). Statements: Some A are B. All B are C. Conclusion: All A being C is a possibility.
Show explanation
Solution. A overlaps B; B inside C. Can all of A sit inside C? Yes — draw A entirely within C, overlapping B; no statement is broken. Possibility follows.
7. The 25-second protocol
For every syllogism:
- Convert each statement to its Venn relationship (All=inside, No=apart, Some=overlap).
- Draw the single most restrictive diagram — add nothing extra.
- Test each conclusion: forced in all diagrams = follows; else check if it's a complementary pair (either–or) or a possibility.
- Watch the three traps: "some" → "all", two negatives → conclusion, and missed either–or pairs.
- For coded sets, decode to words first; for reverse sets, test each option's diagram against all conclusions.
