Definition:Reflexive Closure/Smallest Reflexive Superset

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

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

The reflexive closure of $\mathcal R$ is denoted $\mathcal R^=$.