Definition:Transitive Relation/Definition 1

Definition
Let $\RR \subseteq S \times S$ be a relation in $S$. $\RR$ is transitive :


 * $\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$

that is:
 * $\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \in \RR$

Also see

 * Equivalence of Definitions of Transitive Relation