Definition:Transitive Relation/Definition 1
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Definition
Let $\RR \subseteq S \times S$ be a relation in $S$.
$\RR$ is a transitive relation if and only if:
- $\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$
that is:
- $\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \in \RR$
Also see
- Results about relation transitivity can be found here.
Sources
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