NDA 2023 Maths · Mathematics · Sets, Relations and Functions · hard

The number of symmetric relations that can be defined on a set with 3 elements is

Single correct option

The number of symmetric relations that can be defined on a set with

3

elements is

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Answer: (A) $64$

A symmetric relation is determined by choosing the 3 diagonal pairs freely and, for each of the

\binom32=3

unordered pairs of distinct elements, either both or neither ordered pairs. That gives

3+3=6

independent yes/no choices, so

2^6=64

. The value

512=2^9

counts all relations, symmetric or not.

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