Definition:Transitive Closure (Relation Theory)/Intersection of Transitive Supersets

Definition
Let $\RR$ be a relation on a set $S$.

The transitive closure of $\RR$ is defined as the intersection of all transitive relations on $S$ which contain $\RR$.

The transitive closure of $\RR$ is denoted $\RR^+$.

Also see

 * Equivalence of Definitions of Transitive Closure (Relation Theory)