Reasoning
Syllogisms Guide & Practice
Understand Syllogism Venn Diagram representations, categorical statements (Some/All/No), solved exam questions, and online tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.
Foundation & Concepts
Syllogism is a form of deductive reasoning where a conclusion is drawn from two or more given propositions (premises).
1. Parts of a Proposition
Standard form: Quantifier + Subject + Copula + Predicate
- Quantifier: Specifies quantity (All, No, Some).
- Subject: The word about which something is said.
- Predicate: What is affirmed or denied about the subject.
- Copula: Relationship between subject and predicate (is, are, are not).
2. Four-fold Classification (A, E, I, O)
| Symbol | Proposition | Quantity | Quality | Venn Diagram Hint |
|---|---|---|---|---|
| A | All A are B | Universal | Affirmative | A is entirely inside B |
| E | No A is B | Universal | Negative | A and B are disjoint |
| I | Some A are B | Particular | Affirmative | A and B overlap |
| O | Some A are not B | Particular | Negative | Part of A is outside B |
Patterns/Rules
1. Immediate Inferences (Single Statement)
- All A are B (A) → Implies: Some A are B; Converts to: Some B are A.
- No A is B (E) → Implies: Some A are not B; Converts to: No B is A.
- Some A are B (I) → Converts to: Some B are A.
- Some A are not B (O) → No definite immediate inference.
2. Mediate Inferences (Two+ Statements)
- Positive + Positive = Positive Conclusion.
- Positive + Negative = Negative Conclusion.
- Negative + Negative = No definite conclusion.
- Particular + Particular = No definite conclusion.
- Alignment: The "Middle Term" (term common to both premises) must be distributed at least once.
3. Complementary Pairs (Either-Or Case)
"Either I or II follows" applies when:
- Both individual conclusions are false/uncertain.
- The subject and predicate are the same in both.
- They form a pair: (I + O), (A + O), or (I + E).
4. Possibility
- If no definite relation exists between two terms, any "Possibility" between them is True.
- If a definite relation exists, a contradicting "Possibility" is False.
Solved Examples
1Solved Example
EasyQ1. Statements:
- All gardens are schools.
- All schools are colleges. Conclusions: I. All gardens are colleges. II. Some gardens are colleges.
2Solved Example
ModerateQ3. Statements:
- Some boys are students.
- All students are teenagers. Conclusions: I. All teenagers are students. II. Some boys are teenagers.
3Solved Example
HardQ5. Statements:
- Some birds are trees.
- Some trees are hens. Conclusions: I. Some birds being hens is a possibility. II. All trees being hens is a possibility.