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.