Definition:Antitransitive Relation

Definition
Let $\mathcal R \subseteq S \times S$ be a relation in $S$. $\mathcal R$ is antitransitive iff:
 * $\left({x, y}\right) \in \mathcal R \land \left({y, z}\right) \in \mathcal R \implies \left({x, z}\right) \notin \mathcal R$

that is:
 * $\left\{ {\left({x, y}\right), \left({y, z}\right)}\right\} \subseteq \mathcal R \implies \left({x, z}\right) \notin \mathcal R$

Also known as
Some sources use the term intransitive.

Also see

 * Transitivity of Relations


 * Transitive Relation
 * Non-transitive Relation