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Syllogism

Two statements in, one guaranteed conclusion out — if you follow the rules.

BankingSSCRailwaysCUETUPSC CSE
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📜 Origin of the word

Greek roots

  • Syn = together
  • Logizesthai = to reason

Meaning: Reasoning things together — a conclusion drawn from two premises.

What?

A deductive argument form with two premises and a conclusion, where the conclusion must follow from the premises regardless of real-world truth.

Why?

It tests whether a candidate can separate what is stated from what is assumed — the core skill behind statement-conclusion, assumption and critical-reasoning questions.

How?

Solve using Venn diagrams: represent each premise as circles, test whether the conclusion holds in every possible diagram, and check 'possibility' cases separately.

Who?

Formalised by Aristotle in the Organon; refined by medieval logicians and modern set theory.

Where?

Appears in Banking (IBPS/SBI), SSC, RRB, CUET General Test and CSAT reasoning sections.

When?

Aristotle, 4th century BCE; standard in Indian competitive exams since the 1990s.

Importance

High-scoring and fully rule-based — with practice, syllogism accuracy can be pushed near 100%, making it a reliable marks bank in reasoning sections.

Beginner explanation

All cats are animals. Tommy is a cat. So Tommy must be an animal. You did not need to meet Tommy — the conclusion is locked in by the two sentences.

NCERT connection

Not an NCERT topic directly; the closest base is Class 11 Mathematics Ch.14 'Mathematical Reasoning' on statements and implications.

UPSC-level explanation

In CSAT, syllogism appears with 'possibility' and 'definitely follows' phrasing. Always ask: is there any valid diagram in which the conclusion fails? If yes, it does not follow.

Memory trick

'No middle term, no conclusion.' And: two negative premises never give a conclusion; two particular premises never give a conclusion.

History

Aristotelian logic dominated Western reasoning for two millennia and was absorbed into modern predicate logic in the 19th century.

Important years & timeline

  1. c. 350 BCE — Aristotle formalises the syllogism
  2. 1847 — Boole's algebraic logic
  3. 1880 — John Venn introduces Venn diagrams

Real-life examples

  • · All doctors are graduates + Some graduates are teachers => 'Some doctors are teachers' does NOT follow.
  • · All A are B + All B are C => All A are C follows.
  • · Some A are B => Some B are A always follows (conversion of particular affirmative).

Current affairs link

Reasoning sections are being adapted to computer-based adaptive formats across banking and railway exams.

Mind map

Syllogism

  • └ Premise types
  • └ Rules
  • └ Venn method
  • └ Traps

Premise types

  • └ All (A)
  • └ No (E)
  • └ Some (I)
  • └ Some not (O)

Rules

  • └ Middle term must be distributed
  • └ No conclusion from two negatives
  • └ No conclusion from two particulars

Traps

  • └ Possibility cases
  • └ Either-or pairs
  • └ Reversed conversions

Summary notes

  • · Four statement types: A (All), E (No), I (Some), O (Some not).
  • · Draw every possible Venn arrangement before deciding.
  • · 'Either-or' applies when two conclusions are complementary and neither alone follows.
  • · Real-world truth is irrelevant; only logical necessity counts.

Previous year questions

  • IBPS PO · 2023

    Statements: All pens are books. Some books are pencils. Conclusions: I. Some pens are pencils. II. Some pencils are books.

  • UPSC CSAT · 2020

    Consider the given statements and decide which of the conclusions logically follow.

  • SSC CGL · 2022

    Statements-conclusions question based on 'No X is Y'.

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