# Category:Definitions/Reflexive Transitive Closures

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This category contains definitions related to Reflexive Transitive Closures.
Related results can be found in Category:Reflexive Transitive Closures.

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

### Smallest Reflexive Transitive Superset

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

### Reflexive Closure of Transitive Closure

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

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

### Transitive Closure of Reflexive Closure

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

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

## Pages in category "Definitions/Reflexive Transitive Closures"

The following 4 pages are in this category, out of 4 total.