# Definition:Reflexive Transitive Closure/Smallest Reflexive Transitive Superset

## Definition

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

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

## Also see

• Results about reflexive transitive closures can be found here.