Syllogism – Study Notes
Subject: Reasoning Ability
Exam: Civil Judge (Central & State)
Format: Multiple‑choice / True‑/False / Fill‑in‑the‑blank
1. Simple Explanation
A syllogism is a deductive reasoning pattern that uses two premises to arrive at a conclusion.
It is like a short “if‑then” chain of logic.
| Term | Meaning |
|---|---|
| Premise | A statement that is assumed to be true. |
| Conclusion | The logical result that follows from the premises. |
| Premise 1 (P1) | The first premise. |
| Premise 2 (P2) | The second premise. |
| Conclusion (C) | The statement that logically follows. |
General structure:
P1: All A are B.
P2: All C are A.
C: Therefore, all C are B.
Syllogisms are tested in propositional (simple) and categorical (with quantifiers) forms.
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Quantifiers | All/No/Some determine the type of syllogism (A, E, I, O). |
| 2 | Form | 4‑letter code (e.g., AAA‑1) indicates the form & figure. |
| 3 | Figure | The arrangement of the middle term (M) in P1 & P2 (4 figures). |
| 4 | Validity Rules | 1) Middle term must be distributed once. 2) Contradictory or exclusive premises invalid. 3) If premise is negative, conclusion must be negative. |
| 5 | Distribution | A term is distributed if it refers to all members of its class. |
| 6 | Common Error | Confusing universal vs particular conclusions. |
| 7 | Shortcuts | • Check if conclusion is universal or particular. • Verify distribution of middle term. |
| 8 | Practice | Solve 5–10 problems a day; focus on all 4 figures. |
Quick Reference Table – 4 Figures (All Positive Premises)
| Figure | P1 | P2 | Conclusion |
|---|---|---|---|
| 1 | M → P | S → M | S → P |
| 2 | P → M | S → M | S → P |
| 3 | M → P | M → S | S → P |
| 4 | P → M | M → S | S → P |
(M = Middle Term, P = Predicate, S = Subject)
3. Worked Example
Question
All architects are designers.
Some managers are architects.
Conclusion: Some managers are designers.
Is the conclusion true?
Step‑by‑Step
-
Identify terms
- M (Middle term) = architect
- P (Predicate) = designer
- S (Subject) = manager
-
Translate premises
- P1: All M are P → All architects → designers.
- P2: Some S are M → Some managers → architects.
-
Check validity rules
- Rule 1 – Distributive Middle Term
- Middle term M is not distributed in either premise (neither “All” nor “No” applies to it).
- Violation → Syllogism invalid.
- Rule 1 – Distributive Middle Term
-
Conclusion
- Since the syllogism is invalid, the conclusion cannot be guaranteed.
- The answer: False / Not necessarily true.
Quick Verdict
Conclusion is FALSE (the syllogism is invalid due to non‑distributed middle term).
4. Common Syllogism Patterns (A‑E‑I‑O)
| Pattern | Premise 1 | Premise 2 | Conclusion |
|---|---|---|---|
| A (Universal affirmative) | All A are B | All C are A | All C are B |
| E (Universal negative) | No A are B | All C are A | No C are B |
| I (Particular affirmative) | Some A are B | All C are A | Some C are B |
| O (Particular negative) | No A are B | Some C are A | No C are B |
Tip:
- If both premises are positive → conclusion must be positive.
- If one premise is negative → conclusion must be negative.
5. Quick Revision Summary
| Section | What to Check |
|---|---|
| 1. Identify Terms | S, M, P |
| 2. Determine Quantifiers | All / No / Some |
| 3. Figure | 1, 2, 3, or 4 |
| 4. Distribution | Is M distributed in P1 & P2? |
| 5. Validity Rules | • Middle term distributed at least once. • Negative premise → negative conclusion. • Contradictory premises → invalid. |
| 6. Conclusion Type | Universal vs Particular |
| 7. Practice | 10+ questions per figure daily |
6. Quick Practice Questions (Answer Key)
| # | Question | Answer |
|---|---|---|
| 1 | All A are B. Some C are A. Therefore, Some C are B. | True |
| 2 | No A are B. All C are A. Therefore, No C are B. | True |
| 3 | Some A are B. All C are A. Therefore, Some C are B. | True |
| 4 | All A are B. No C are A. Therefore, No C are B. | True |
| 5 | Some A are B. Some C are A. Therefore, Some C are B. | Cannot be determined |
| 6 | No A are B. Some C are A. Therefore, No C are B. | Cannot be determined |
| 7 | All A are B. Some |