Definition:Transitive with Respect to a Relation

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Definition

Let $A$ be a class.

Let $\RR$ be a relation on $A$.

Let $S$ be a set.


Then $S$ is transitive with respect to $\RR$ if and only if:

$\forall x \in A: \forall y \in S: \paren {x \mathrel \RR y \implies x \in S}$


Sources