Definition:Asymmetric Relation/Definition 1

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

$\mathcal R$ is asymmetric :


 * $\left({x, y}\right) \in \mathcal R \implies \left({y, x}\right) \notin \mathcal R$

Also see

 * Equivalence of Definitions of Asymmetric Relation