Inverse of Symmetric Relation is Symmetric

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Theorem

Let $\RR$ be a relation on a set $S$.


If $\RR$ is symmetric, then so is $\RR^{-1}$.


Proof

Let $\RR$ be symmetric.

Then from Relation equals Inverse iff Symmetric it follows that $\RR^{-1}$ is also symmetric.

$\blacksquare$