Syllogism — Study Notes for IBPS Clerk Prelims
Overview
Syllogism is one of the most predictable and scoring topics in the IBPS Clerk Reasoning section. Each set presents two statements followed by conclusions, and you must determine which conclusions logically follow.
The topic tests your ability to understand relationships between groups (sets) expressed through quantifiers like "All," "Some," "No," and "Some not." Unlike puzzles that can be time-consuming, syllogism questions can be solved quickly once you master the rules—making them ideal for boosting your score within tight time limits.
For Clerk Prelims, the syllogism questions stay at a moderate difficulty level. You won't encounter complex three-statement syllogisms or "possibility" cases frequently seen in PO exams. Focus on mastering the standard rules, and you can attempt these questions with near-perfect accuracy.
Key Concepts
- Statements establish relationships between two groups using quantifiers. Think of each group as a circle, and the quantifier tells you how these circles overlap.
- Four standard quantifiers exist: All (complete inclusion), Some (partial overlap), No (complete exclusion), and Some not (partial exclusion).
- "All A are B" does not mean "All B are A." Direction matters—if all dogs are animals, it doesn't mean all animals are dogs.
- "Some" implies at least one, possibly all. When a statement says "Some A are B," it means one or more A could be B, including the possibility that all A are B.
- "No" is a complete denial and works both ways. "No A is B" automatically means "No B is A."
- Conclusions must be 100% certain from the given statements. If a conclusion is only sometimes true, it does not follow.
- Venn diagrams are the most reliable solving method for beginners. Draw circles representing groups and shade/overlap them according to statements.
- Complementary pairs: If "Some A are B" is false, then "No A is B" is true, and vice versa.
Formulas / Key Facts
Standard Conversion Rules:
| Original Statement | Valid Conversion |
|---|---|
| All A are B | Some B are A (valid) |
| Some A are B | Some B are A (valid) |
| No A is B | No B is A (valid) |
| Some A are not B | No valid conversion |
Deduction Rules (When Two Statements Combine):
| Statement 1 | Statement 2 | Valid Conclusion |
|---|---|---|
| All A are B | All B are C | All A are C; Some C are A |
| All A are B | Some B are C | No definite conclusion about A and C |
| 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 |
| Some A are B | No B is C | Some A are not C |
| No A is B | All B are C | Some C are not A |
Quick Memory Aid:
- All + All = All
- All + No = No
- Some + All = Some
- Some + No = Some not
- Some + Some = No conclusion
- All + Some = No conclusion
Worked Examples
Example 1: Basic Two-Statement Problem
Statements:
- All pens are pencils.
- All pencils are erasers.
Conclusions: I. All pens are erasers. II. Some erasers are pens.
Solution:
- Draw three circles: Pens inside Pencils, Pencils inside Erasers.
- Since Pens ⊂ Pencils ⊂ Erasers, all pens must be erasers. → Conclusion I follows.
- If all pens are erasers, then some erasers are definitely pens. → Conclusion II follows.
Answer: Both I and II follow.
Example 2: Negative Statement
Statements:
- Some cats are dogs.
- No dog is a rat.
Conclusions: I. Some cats are not rats. II. No cat is a rat.
Solution:
- "Some cats are dogs" means there's an overlap between cats and dogs.
- "No dog is a rat" means dogs and rats are completely separate.
- Those cats that are dogs cannot be rats. → Some cats are not rats. Conclusion I follows.
- But cats that are NOT dogs could still be rats (not restricted by statements). → Conclusion II does not follow.
Answer: Only I follows.
Example 3: Either-Or Case
Statements:
- All books are pages.
- Some pages are covers.
Conclusions: I. Some books are covers. II. No book is a cover.
Solution:
- All books are pages, and some pages are covers.
- The pages that are covers may or may not include the books. No definite link.
- Conclusion I: Not definite → Does not follow.
- Conclusion II: Not definite → Does not follow.
- But I and II are complementary pairs (if one is false, the other must be true in reality). Since we cannot determine which, either I or II follows.
Answer: Either I or II follows.
Common Mistakes
- Reversing "All" statements incorrectly → "All A are B" does NOT mean "All B are A." Only convert to "Some B are A."
- Treating "Some" as "Only Some" → "Some A are B" includes the possibility that all A are B. Don't assume some are excluded.
- Ignoring the "Some not" dead-end → "Some A are not B" cannot be converted or combined productively. Don't force conclusions from it.
- Confusing definite with possible → A conclusion must ALWAYS be true from the statements. If it's true only in one diagram version, it doesn't follow.
- Missing the Either-Or case → When two conclusions are complementary (one positive, one negative about the same relationship) and neither follows individually, check if "Either-Or" applies.
Quick Reference
- All + All = All; All + No = No; Some + All = Some; Some + No = Some not.
- "No" is reversible; "All" converts to "Some" (reversed); "Some not" has no valid conversion.
- Draw Venn diagrams for accuracy—speed comes with practice.
- Either-Or applies when conclusions are a complementary pair and neither follows alone.
- Some = At least one, possibly all. Never assume exclusion.
- If no common term links the two statements, no conclusion can be drawn between the end terms.