# Definition:Reflexive Closure/Smallest Reflexive Superset

## Definition

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

The reflexive closure of $\RR$ is defined as the smallest reflexive relation on $S$ that contains $\RR$ as a subset.

The reflexive closure of $\RR$ is denoted $\RR^=$.

## Also see

• Results about reflexive closures can be found here.