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Lines of Symmetry

Question

Number of relation from A to A which are both reflexive and symmetric is

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Solution

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A relation has ordered pairs $(a, b) .$ Reflexive and symmetric Relations means $(a, a)$ is included in $R$ and $(a, b) (b, a)$ pairs can be included or not. (In Symmetric relation for pair $(a, b) (b, a)$ (considered as a pair). whether it is included in relation or not) So total number of Reflexive and symmetric Relations is $2^{\frac{n^{2} - n}{2}}$

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