Definition:Reflexive Transitive Closure/Smallest Reflexive Transitive Superset
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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.
Sources
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): Appendix $\text{A}.4$: Definition $\text{A}.21$