Inverse of Symmetric Relation is Symmetric
Jump to navigation
Jump to search
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.
$\blacksquare$