Definition:Right Quasi-Reflexive Relation
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Definition
Let $\RR \subseteq S \times S$ be a relation in $S$.
Definition 1
$\RR$ is right quasi-reflexive if and only if:
- $\forall x, y \in S: \tuple {x, y} \in \RR \implies \tuple {y, y} \in \RR$
Definition 2
$\RR$ is right quasi-reflexive if and only if:
- $\forall y \in \Img \RR: \tuple {y, y} \in \RR$
where $\Img \RR$ denotes the image set of $\RR$.
Also see
- Results about right quasi-reflexive relations can be found here.