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

Jump to navigation
Jump to search

## Definition

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

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

- $\mathcal R^* = \left({\mathcal R^+}\right)^=$