Definition:Transitive with Respect to a Relation

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 $\RR$ :


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