Definition:Coreflexive Relation

Definition

Let $\mathcal R \subseteq S \times S$ be a relation in $S$.

$\mathcal R$ is coreflexive (pronounced co-reflexive, not core-flexive) iff:

$\forall x, y \in S: \left({x, y}\right) \in \mathcal R \implies x = y$

Also see

• Reflexivity of Relations

• Reflexive Relation
• Antireflexive Relation
• Non-reflexive Relation

• Results about reflexivity of relations can be found here.