Definition:Symmetric Closure/Definition 1

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

The symmetric closure of $\RR$ is denoted $\RR^\leftrightarrow$, and is defined as the union of $\RR$ with its inverse:


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

Also see

 * Equivalence of Definitions of Symmetric Closure