Syllogism: Reasoning Ability Notes for Delhi Patwari / Lekhpal

Syllogism – Reasoning Ability

Delhi Patwari / Lekhpal – Examination Guide

A syllogism is a form of logical reasoning that uses two (or more) premises to arrive at a conclusion.

Premise 1 (Major Premise) – a general statement.
Premise 2 (Minor Premise) – a specific statement that falls under the general category.
Conclusion – a logical inference that follows necessarily from the two premises.

Example
All mammals are warm‑blooded.
All dogs are mammals.
Therefore, all dogs are warm‑blooded.

Feature	Description
Logical Validity	Conclusion must necessarily follow from premises.
Logical Soundness	Premises must be true and the reasoning valid.
Categories	C – universal affirmative; D – universal negative; E – particular affirmative; I – particular negative.
Quantifiers	All, Some, No, None
Quality	Affirmative vs Negative
Quantity	Universal vs Particular

Symbol	Form	Example
AA‑1	All A are B. All B are C. → All A are C.	All birds are animals. All animals are living beings. → All birds are living beings.
AE‑1	All A are B. Some B are not C.	All cars are vehicles. Some vehicles are not electric.
EA‑1	Some A are B. All B are C.	Some fruits are apples. All apples are sweet.
EE‑1	Some A are B. Some A are not C.	Some birds can fly. Some birds cannot fly.
OI‑1	No A are B. Some C are A.	No reptiles are mammals. Some animals are reptiles.
OI‑2	No A are B. Some C are B.	No birds are mammals. Some pets are birds.
II‑1	Some A are B. Some A are not C.	Some students are athletes. Some students are not athletes.
II‑2	Some A are B. Some C are not B.	Some flowers are roses. Some plants are not roses.

Note: The above table shows the most common forms. In exams you might encounter variations, but the core logic remains the same.

Identify the Premises
- Label them as Major and Minor (or First and Second).
Determine the Type
- Check the quantifier (All / Some / No) and the quality (Affirmative / Negative).
Apply the Rules
- Use the standard syllogistic rules (e.g., Major Premise determines the Conclusion’s subject, Minor Premise determines the Conclusion’s predicate).
Check for Validity
- Make sure the conclusion logically follows.
- Verify No contradictions (e.g., “All A are B” and “No B are C” cannot both be true if an A exists that is also a C).

Rule	What It Means
Rule of Quantity	If the conclusion is universal, at least one premise must be universal.
Rule of Quality	If the conclusion is negative, at least one premise must be negative.
Rule of Distribution	The conclusion cannot refer to a term that was undetermined (undistributed) in both premises.
Rule of Subalternation	From a universal premise you can infer a particular one, but not vice versa.

Premise 1: All A are B.
Premise 2: No B are C.
Conclusion: All A are not C.

Step	Action	Reason
1	Label the premises	1 = Major, 2 = Minor
2	Identify quantifiers & quality	Premise 1 = Universal affirmative (All A are B). Premise 2 = Universal negative (No B are C).
3	Apply the Rule of Quantity	Conclusion must be universal (cannot be particular).
4	Apply the Rule of Quality	Since at least one premise is negative, conclusion may be negative.
5	Check distribution	In Premise 1, “B” is distributed (All B). In Premise 2, “B” is also distributed. The term “B” is fully distributed in both premises, so the conclusion “All A are not C” is valid.
6	Final conclusion	All A are not C.

Interpretation: If every A is a B, and no B is a C, then indeed no A can be a C.

Mistake	Why It Happens	How to Avoid
Confusing the order	Mixing up which premise is major/minor	Write them in order and keep track of subject/predicate
Ignoring distribution	Forgetting that all and no distribute the predicate	Check distribution after each premise
Assuming truth of premises	Validity ≠ Soundness	Treat premises as given; only check logical flow
Choosing wrong conclusion type	Picking a particular conclusion when the premises are universal	Apply the Rule of Quantity first
Over‑generalising	Assuming a particular conclusion from a universal premise	Remember subalternation goes one way only