Definition:Symmetric Closure/Definition 1

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Definition

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


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

$\mathcal R^\leftrightarrow = \mathcal R \cup \mathcal R^{-1}$