Definition:Reflexive Closure/Intersection of Reflexive Supersets
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Definition
Let $\RR$ be a relation on a set $S$.
Let $\QQ$ be the set of all reflexive relations on $S$ that contain $\RR$.
The reflexive closure of $\RR$ is denoted $\RR^=$, and is defined as:
- $\RR^= := \bigcap \QQ$
That is:
- $\RR^=$ is the intersection of all reflexive relations on $S$ containing $\RR$.
Also see
- Results about reflexive closures can be found here.