Syllogisms & Inequality Statements

Syllabus Unit: Reasoning Ability

Why it matters

Chapter overview

Syllogisms and inequality-based reasoning form a predictable block in SBI PO Reasoning built entirely on Venn-diagram and chaining logic — every question gives 2-3 statements and asks which conclusions definitely follow, and the exam rewards drawing every possible diagram or case, not just the most obvious one.

Preliminary Examination Syllabus Reasoning Ability 35% weightage

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Identify each statement's type

Draw all valid Venn diagrams

Test each conclusion against every diagram

Conclusion holds only if true in ALL diagrams

1Syllogisms (All, Some, None)

Two or three statements, drawn as Venn circles, decide every conclusion — the diagram is the proof, not intuition.

Learning Objectives

State the four standard categorical statement types: All A are B, No A is B, Some A are B, Some A are not B.
Draw every Venn diagram consistent with two given statements, not just the most obvious one.
Test a conclusion by checking whether it holds in EVERY valid diagram, not just the first one drawn.
Apply the standard combination rules: 'All + All = All', 'All + No = No', 'Some + All = Some' through a shared middle term.

Key Terms

Categorical StatementOne of the four standard forms: universal affirmative (All A are B), universal negative (No A is B), particular affirmative (Some A are B), particular negative (Some A are not B).

Venn Diagram MethodDrawing all circle arrangements consistent with the given statements, then checking which conclusions hold true in every one of those valid diagrams.

Middle TermThe term common to both statements (e.g., 'pencils' in 'All pens are pencils; some pencils are erasers') used to connect the two statements into one conclusion.

Complementary PairTwo conclusion types that together cover every logical possibility between two terms — the trigger condition for the either-or rule.

A syllogism gives 2-3 categorical statements and asks which conclusions must be true. The entire question is decided by Venn diagrams: a conclusion is valid only if it holds in every diagram consistent with the statements, not merely in the most natural-looking one.

The four statement types

All A are B — universal affirmative; every A is inside B, but B may extend beyond A.
No A is B — universal negative; the A and B circles have zero overlap.
Some A are B — particular affirmative; A and B overlap by at least one element, but neither must be fully inside the other.
Some A are not B — particular negative; at least part of A lies outside B.

Drawing every valid diagram

Particular ('Some') statements admit multiple diagrams — partial overlap, or one circle fully inside the other. Worked example: 'All pens are pencils; some pencils are erasers' — pencils could overlap erasers only outside the pen region, or could overlap right through the pen region too. Since both are valid, 'Some pens are erasers' is NOT guaranteed, but 'Some erasers are pencils' (the direct converse of the second statement) always holds.

Some A are B ⟹ Some B are A (always valid conversion). All A are B ⇏ All B are A (never assume this).

Common MistakeTrap: drawing only the 'most likely-looking' diagram and missing an alternate, equally valid diagram that breaks a conclusion — always ask 'could the circles also be arranged this other way?' before accepting a conclusion.

Exam Tip'Some A are B' always converts to 'Some B are A' — but 'All A are B' never automatically converts to 'All B are A'. Confusing these two conversion rules is the single most common syllogism error.