Category:Symmetric Closures

This category contains results about Symmetric Closures.
Definitions specific to this category can be found in Definitions/Symmetric Closures.

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

Definition 1

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

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

Definition 2

The symmetric closure of $\RR$ is denoted $\RR^\leftrightarrow$, and is defined as the smallest symmetric relation on $S$ which contains $\RR$.