Symmetric Closure of Inverse Relation

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

Let $\RR^{-1}$ be the inverse of $\RR$.

Let $\RR^\leftrightarrow$ be the symmetric closure of $\RR$.

Then:


 * $\RR^\leftrightarrow = \paren {\RR^{-1} }^\leftrightarrow$