JEE Main 2025 Jan 22 Shift 1, Mathematics Q1: Relations

JEE Main2025Jan 22, Shift 1Mathematics

The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :

Solution

The number of equivalence relations on a finite set equals the number of partitions of that set (the Bell number).

For a 3-element set, the partitions are:

$∙$ ${{1, 2, 3}}$ (one block)

$∙$ ${{1, 2}, {3}}$ , ${{1, 3}, {2}}$ , ${{2, 3}, {1}}$ (one pair plus a singleton)

$∙$ ${{1}, {2}, {3}}$ (three singletons)

Total $= 1 + 3 + 1 = 5$ .

Concept behind this question

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