Symmetric Closure of Inverse Relation

Definition
Let $\mathcal R$ be a relation on a set $S$.

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

Let $\mathcal R^\leftrightarrow$ be the symmetric closure of $\mathcal R$.

Then:


 * $\mathcal R^\leftrightarrow = \left({\mathcal R^{-1}}\right)^\leftrightarrow$