Definition:Left Quasi-Reflexive Relation

Definition

Let $\RR \subseteq S \times S$ be a relation in $S$.

Definition 1

$\RR$ is left quasi-reflexive if and only if:

$\forall x, y \in S: \tuple {x, y} \in \RR \implies \tuple {x, x} \in \RR$

Definition 2

$\RR$ is left quasi-reflexive if and only if:

$\forall x \in \Dom \RR: \tuple {x, x} \in \RR$

where $\Dom \RR$ denotes the domain of $\RR$.

Also see

• Equivalence of Definitions of Left Quasi-Reflexive Relation

• Definition:Right Quasi-Reflexive Relation
• Definition:Quasi-Reflexive Relation

• Results about left quasi-reflexive relations can be found here.