Syllogism: Reasoning Ability Notes for Madhya Pradesh TET (Teacher Eligibility)

Syllogism – Study Notes for Madhya Pradesh TET (Reasoning Ability)

Audience: Students preparing for competitive exams (IIT‑JEE, JEE‑Main, State‑TET, UPSC, etc.)
Style: Exam‑oriented, rigorous, with derivations, key formulae, pitfalls, and a hard‑level practice problem.

1. What is a Syllogism?

A syllogism is a logical argument that comprises three statements:

Symbol	Meaning	Example
Premise 1 (P1)	Primary premise	All A are B
Premise 2 (P2)	Secondary premise	All B are C
Conclusion (C)	Deductive result	All A are C

The classic syllogism is categorical (involving categories of objects) but the term also covers hypothetical (if‑then) and disjunctive (either‑or) forms.

2. Types of Syllogisms

Type	Primary Feature	Example
Categorical	Uses categorical propositions (All, No, Some)	All A are B; Some B are C; → Some A are C
Hypothetical (Conditional)	Uses “If‑then” statements	If A then B; If B then C; → If A then C
Disjunctive	Uses “Either‑or” (inclusive or exclusive)	Either A or B; Not A; → B

Tip:
Categorical syllogisms dominate reasoning tests.
Hypothetical and disjunctive syllogisms are fewer but often trick candidates because of the subtle use of “either” vs. “or”.

3. Rules of Validity for Syllogisms

Rule	Statement	Why it matters
Distribution	A term is distributed if the proposition covers all members of the term’s class.	Ensures correct inference.
Reversing	You cannot reverse a universal affirmative (All A are B) to “All B are A” unless you know the two classes are equivalent.	Many fallacies arise from this.
Minor Premise	The conclusion cannot be more specific than the premises.	Avoids “logical leaps”.
Middle Term	The middle term (B in the example above) must appear in both premises.	Without it, the syllogism is invalid.
Mood & Figure	A syllogism’s mood (the pattern of A, E, I, O propositions) and figure (the arrangement of terms) determine validity.	There are only 256 possible moods; 24