Syllogism — IBPS PO Prelims Study Notes

Overview

Syllogism is one of the most predictable scoring topics in IBPS PO Prelims Reasoning section. Every exam features 3–5 questions based on logical deductions from two or three statements using quantifiers like "All," "Some," "No," and "Only." Unlike puzzles that can be time-consuming, syllogism questions follow fixed logical rules — once you master them, you can solve each question in under 60 seconds.

The topic tests your ability to draw valid conclusions from given premises without adding personal assumptions. IBPS PO frequently includes both direct syllogism (derive conclusions from statements) and reverse syllogism (find which statement makes a given conclusion valid). Mastering Venn diagram representation is the fastest and most reliable approach for exam conditions.

Key Concepts

• **Universal Affirmative (A-type): "All A are B"** — Every member of A belongs to B. A is completely inside B, but B may extend beyond A.

• **Universal Negative (E-type): "No A is B"** — There is zero overlap between A and B. The two circles never touch.

• **Particular Affirmative (I-type): "Some A are B"** — At least one A is B. There is partial overlap; could also mean all A are B (some includes all as a possibility).

• **Particular Negative (O-type): "Some A are not B"** — At least one A exists outside B. Part of A does not overlap with B.

• **"Only A are B" = "All B are A"** — This reversal is a common trap. "Only teachers are graduates" means all graduates are teachers, not the other way around.

• **Complementary Pairs** — "All A are B" and "Some A are not B" cannot both be true simultaneously. Similarly, "No A is B" and "Some A are B" are contradictory.

• **Possibility Conclusions** — When a definite conclusion doesn't follow, check if "Some A may be B" or "All A being B is a possibility" can be true based on open regions in your Venn diagram.

Formulas / Key Facts

| Statement Type | Notation | Conversion Rule | |----------------|----------|-----------------| | All A are B | A-type | Converts to "Some B are A" (I-type) | | No A is B | E-type | Converts to "No B is A" (E-type) | | Some A are B | I-type | Converts to "Some B are A" (I-type) | | Some A are not B | O-type | No valid conversion possible |

**Deduction Rules (Combining Two Statements):**

• A + A = A (All A are B + All B are C → All A are C)
• A + E = E (All A are B + No B is C → No A is C)
• A + I = No definite conclusion
• E + I = O (No A is B + Some B are C → Some C are not A)