# Definition:Reflexive Transitive Closure/Transitive Closure of Reflexive Closure

## Definition

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

The reflexive transitive closure of $\RR$ is denoted $\RR^*$, and is defined as the transitive closure of the reflexive closure of $\RR$:

$\RR^* = \paren {\RR^=}^+$

## Also see

• Results about reflexive transitive closures can be found here.