Competitive exam reasoning

Syllogism and Inequality Shortcuts

These questions ask what must be true, not what looks likely. Use set diagrams for syllogisms and rewrite coded comparisons into ordinary symbols before building a chain.

1

Treat ‘all’ as containment

If all A are B, draw A inside B. Membership can move from A to B, but the statement cannot be reversed.

Solved exampleAll roses are flowers and all flowers are plants, so all roses are plants.
Common trapIt does not follow that all flowers are roses.
2

Give ‘some’ a witness

Some A are B means at least one item belongs to both groups. Carry that same item through any valid containment statement.

Solved exampleAll poets are readers and some poets are teachers, so some readers are teachers.
Common trap‘Some’ does not mean ‘some but not all’.
3

Reject necessity with a counterexample

A conclusion follows only if every arrangement satisfying the premises also satisfies it. One valid counter-diagram is enough to reject it.

Solved exampleAll A are B and all C are B does not force any A to be C; the two groups may occupy separate parts of B.
Common trapDo not assume that universal groups contain members unless the exam states that convention.
4

Join inequalities in one direction

Comparisons can be combined when their shared terms form one consistent chain.

Solved exampleA ≥ B and B > C imply A > C.
Common trapA > B < C provides no comparison between A and C.
5

Decode symbols before solving

Replace every custom symbol with >, <, =, ≥ or ≤, and only then test transitivity or either-or conclusions.

Solved exampleIf # means ≥ and @ means <, A # B @ C becomes A ≥ B < C; A versus C remains unknown.
Common trapThe visual shape of a custom symbol has no mathematical meaning.

Frequently asked questions

When does a syllogism conclusion follow?

It follows only when it is true in every set arrangement permitted by the premises.

Can inequalities be joined through a common term?

Yes when the signs create one continuous direction, such as A ≥ B > C. Opposing branches such as A > B < C cannot be joined.