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