Syllogism

Syllogism – Reasoning Ability

(For Uttarakhand Police Constable Examination)

1️⃣ Simple Explanation

A syllogism is a short logical argument that has two premises (statements) and a conclusion that follows necessarily from those premises.

Structure

• Premise 1
• Premise 2
• Conclusion

If both premises are true, the conclusion must also be true. Syllogisms test your ability to see the logical relationship between statements.

2️⃣ Key Points & Rules

• All / No → Universal
• Some → Particular | Determines how inference is made. | | 4 | Subject & Predicate | The subject of the conclusion must appear in at least one premise. | | 5 | No circular reasoning | The conclusion must not repeat the premises. | | 6 | Logical validity | If premises are true, conclusion cannot be false. | | 7 | Types of Syllogisms | - Categorical (e.g., “All A are B”)
  - Hypothetical (if‑then statements)
  - Disjunctive (either‑or statements) | | 8 | Common patterns | 1. All A are B + All B are C → All A are C
  2. All A are B + No C are A → No C are B
  3. If A then B + If B then C → If A then C | | 9 | Avoiding pitfalls | - Wrong subject: conclusion’s subject must be present.
  - Assuming equivalence: “All A are B” does not mean “All B are A”. | | 10 | Answer format | Usually multiple‑choice: pick the only logically valid conclusion. |

3️⃣ Worked Example

Problem

Premise 1: All students are diligent.
Premise 2: All diligent people are punctual.
Question: Which of the following is a valid conclusion?

1. All students are punctual.
2. All punctual people are students.
3. Some students are punctual.
4. No students are punctual.

Solution

1. Identify quantifiers

   • Premise 1: Universal (All)
   • Premise 2: Universal (All)

2. Apply transitive property

   • From (1) → Students ⊆ Diligent
   • From (2) → Diligent ⊆ Punctual
   • Combine → Students ⊆ Punctual

3. Check each choice

   • 1. All students are punctual → True (matches conclusion).
   • 2. All punctual people are students → False (reverse direction).
   • 3. Some students are punctual → True, but not the only valid conclusion; the question asks for the conclusion.
   • 4. No students are punctual → False.

Answer: 1. All students are punctual.

Key Reasoning Steps

4️⃣ Quick Revision Summary

• Definition: Short reasoning with 2 premises → 1 conclusion.
• Universal: All / No → applies to every member of the set.
• Particular: Some → applies to at least one member.
• Common patterns:
  • All A → B, All B → C → All A → C
  • All A → B, No C → A → No C → B
  • If A → B, If B → C → If A → C
• Key checks:
  • Subject of conclusion appears in a premise.
  • Conclusion must be logically necessary, not just possible.
  • Avoid reverse inference unless both directions are given.
• Problem‑solving tip: Write the premises in set notation (A⊆B) and derive the conclusion quickly.

Practice Tip
Create your own syllogisms daily:

1. Write two premises.
2. Write a valid conclusion.
3. Try to find a false conclusion and explain why it fails.

Happy studying!