NDA 2025 Maths · Mathematics · Sets, Relations and Functions · hard

The number of relations on a set of 4 elements that are both reflexive and symmetric is

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Answer: (C) $64$

Reflexivity fixes the 4 diagonal pairs. Symmetry means each of the

\binom42=6

unordered off-diagonal pairs is either in both directions or absent, giving

2^6=64

choices. Counting all

2^{10}

pairs would give the symmetric-only answer

1024

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