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)
• I + I = No definite conclusion
• E + E = No definite conclusion

**Critical Fact:** "Some" in syllogism means "at least one" and includes the possibility of "all."

**Only/All Conversion:** "Only A are B" = "All B are A" = "No non-A is B"

Worked Examples

**Example 1: Basic Two-Statement Syllogism**

*Statements:* 1. All dogs are animals. 2. All animals are living beings.

*Conclusions:* I. All dogs are living beings. II. Some living beings are dogs.

*Solution:*

• Draw: Dogs completely inside Animals, Animals completely inside Living Beings.
• Dogs is entirely within Living Beings → Conclusion I follows.
• Since some part of Living Beings contains Dogs → Conclusion II follows.
• **Answer: Both I and II follow.**

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**Example 2: Negative Statement**

*Statements:* 1. All roses are flowers. 2. No flower is a thorn.

*Conclusions:* I. No rose is a thorn. II. Some thorns are roses.

*Solution:*

• Draw: Roses inside Flowers. Thorns completely separate from Flowers.
• Since Roses are inside Flowers and Thorns don't touch Flowers → No rose is a thorn. Conclusion I follows.
• Thorns and Roses have zero overlap → "Some thorns are roses" is false. Conclusion II doesn't follow.
• **Answer: Only I follows.**

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**Example 3: Reverse Syllogism**

*Conclusion given:* Some cats are dogs.

*Which statement(s) must be true?* A. All cats are dogs. B. All dogs are cats. C. Some dogs are cats. D. No cat is a dog.

*Solution:*

• If "Some cats are dogs" is true, the sets overlap.
• "Some dogs are cats" is the converse of an I-type statement and is always valid.
• "All cats are dogs" may or may not be true (not necessary).
• "No cat is a dog" directly contradicts the conclusion.
• **Answer: C must be true.**

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**Example 4: Possibility-Based**

*Statements:* 1. Some pens are pencils. 2. All pencils are erasers.

*Conclusions:* I. All pens being erasers is a possibility. II. Some erasers are pens.

*Solution:*

• The overlapping portion of pens-and-pencils is inside erasers.
• Can pens be entirely inside erasers? Yes — the diagram allows this possibility. Conclusion I follows.
• The pens-pencils overlap is inside erasers → Some erasers are definitely pens. Conclusion II follows.
• **Answer: Both I and II follow.**

Common Mistakes

• **Treating "Some" as "Only Some"** → "Some A are B" does NOT mean "Some A are not B." In logic, "some" includes the possibility of "all." Always check both scenarios.

• **Confusing "Only" with "All"** → "Only cats are pets" does NOT mean "All cats are pets." It means "All pets are cats." Draw the Venn diagram with pets inside cats.

• **Forcing a conclusion from two particular statements** → Two I-type statements (Some-Some) never give a definite conclusion. Don't guess — mark "no conclusion follows."

• **Ignoring possibility conclusions** → When a definite conclusion fails, IBPS often asks about possibilities. If regions don't overlap but aren't explicitly separated, "may be" conclusions can follow.

• **Converting O-type statements** → "Some A are not B" has NO valid converse. You cannot conclude "Some B are not A" from it.

Quick Reference

• **All A are B** → A sits completely inside B.
• **No A is B** → A and B circles never touch.
• **Some A are B** → Circles overlap; could overlap completely.
• **Only A are B = All B are A** — memorize this conversion.
• **Two negative statements** → No definite conclusion ever.
• **Possibility is true** when the diagram doesn't explicitly prevent the relationship.