Syllogism — Study Notes for SBI Clerk Prelims
Overview
These questions test your ability to draw valid logical conclusions from two given statements using universal and particular quantifiers (All, Some, No, Only).
The good news: syllogism follows strict, predictable rules. Once you master the Venn diagram method, you can solve these questions quickly and accurately—often in under 30 seconds each. The challenge lies in avoiding over-conclusion (deriving more than what logically follows) and handling tricky "Only" statements correctly.
For SBI Clerk level, you'll encounter standard two-statement syllogisms with direct conclusions. Possibility-based questions ("Some A may be B") also appear frequently. Master the basics thoroughly before attempting shortcuts.
Key Concepts
- Universal Positive (A-type): "All A are B" — Every member of A belongs to B. A is completely inside B.
- Universal Negative (E-type): "No A is B" — Not a single member of A belongs to B. A and B don't overlap at all.
- Particular Positive (I-type): "Some A are B" — At least one member of A belongs to B. Partial overlap exists.
- Particular Negative (O-type): "Some A are not B" — At least one member of A does not belong to B.
- "Only A are B" = "All B are A": This is a critical conversion. "Only teachers are graduates" means "All graduates are teachers."
- Definite vs Possibility conclusions: A definite conclusion must be true in ALL valid Venn diagrams. A possibility conclusion is true if it holds in AT LEAST ONE valid diagram.
- Complementary pairs: "Some A are B" and "No A is B" are complementary—exactly one must be true. Similarly, "All A are B" and "Some A are not B" are complementary.
Formulas / Key Facts
| Statement Type | Standard Form | Venn Representation |
|---|---|---|
| All A are B | A ⊆ B | Circle A inside Circle B |
| No A is B | A ∩ B = ∅ | Circles don't touch |
| Some A are B | A ∩ B ≠ ∅ | Circles partially overlap |
| Some A are not B | Part of A outside B | A not fully inside B |
Conversion Rules:
- "All A are B" → "Some B are A" (valid)
- "All A are B" → "All B are A" (NOT valid)
- "No A is B" → "No B is A" (valid)
- "Some A are B" → "Some B are A" (valid)
- "Some A are not B" → Cannot be converted
Important Derivations:
- "All A are B" + "All B are C" → "All A are C" and "Some C are A"
- "All A are B" + "No B is C" → "No A is C"
- "Some A are B" + "All B are C" → "Some A are C"
- "Some A are B" + "Some B are C" → No definite conclusion
Remember: Two particular statements (Some + Some) or two negative statements (No + No) give NO definite conclusion.
Worked Examples
Example 1: Basic Two-Statement Problem
Statements:
- All books are pens.
- All pens are erasers.
Conclusions: I. All books are erasers. II. Some erasers are books. III. All erasers are pens.
Solution: Draw Venn diagram: Books (innermost) → Pens (middle) → Erasers (outermost)
- Conclusion I: Books ⊆ Pens ⊆ Erasers, so Books ⊆ Erasers. TRUE
- Conclusion II: Since all books are erasers, at least some erasers are books. TRUE
- Conclusion III: Erasers is the largest set; not all erasers need be pens. FALSE
Answer: Only I and II follow.
Example 2: With Negative Statement
Statements:
- All cats are dogs.
- No dog is a rat.
Conclusions: I. No cat is a rat. II. Some dogs are cats.
Solution: Draw: Cats inside Dogs; Rats completely separate from Dogs.
- Conclusion I: Cats ⊆ Dogs, and Dogs ∩ Rats = ∅, so Cats ∩ Rats = ∅. TRUE
- Conclusion II: Since all cats are dogs, some dogs are definitely cats. TRUE
Answer: Both I and II follow.
Example 3: Possibility Question
Statements:
- Some apples are oranges.
- All oranges are bananas.
Conclusions: I. All apples being bananas is a possibility. II. Some bananas are apples.
Solution: "Some apples are oranges" means partial overlap. Those overlapping apples are inside bananas (since all oranges are bananas).
- Conclusion I: In one valid diagram, the apple circle could be entirely inside bananas. So possibility exists. TRUE
- Conclusion II: The apples that are oranges are definitely bananas. So some bananas are apples. TRUE (Definite)
Answer: Both follow.
Common Mistakes
- "All A are B" means "All B are A" → WRONG. "All A are B" only guarantees "Some B are A." Always remember A is the subset, not B.
- Drawing only one Venn diagram → WRONG when checking definite conclusions. A conclusion is definite only if it's true in EVERY possible valid diagram. Draw multiple configurations.
- Confusing "Only" with "All" → "Only A are B" means "All B are A," not "All A are B." Flip the subject and predicate.
- Concluding from two particular statements → "Some A are B" + "Some B are C" does NOT guarantee "Some A are C." The overlapping B members might be different.
- Ignoring complementary pair logic → In "either-or" type answers, check if two conclusions are complementary (one must be true). Example: "Some A are B" and "No A is B" — exactly one is always true.
- Treating possibility as certainty → "Some A may be B" is NOT the same as "Some A are B." Possibility only requires one valid diagram where it holds.
Quick Reference
- All A are B → Some B are A (always valid conversion)
- No A is B = No B is A (symmetric relationship)
- Only A are B = All B are A (swap and change to All)
- Two negatives or two particulars = No definite conclusion
- Possibility = True in at least one valid diagram; Definite = True in all valid diagrams
- Complementary pairs: (All, Some...not) and (Some, No) — one must be true