Definition:Transitive Relation/Definition 2

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Definition

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

$\mathcal R$ is transitive if and only if:

$\mathcal R \circ \mathcal R \subseteq \mathcal R$

where $\circ$ denotes composite relation.


Also see

  • Results about relation transitivity can be found here.


Sources