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

 * Equivalence of Definitions of Reflexive Transitive Closure