Definition:Asymmetric Relation/Definition 2

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

$\mathcal R$ is asymmetric it and its inverse are disjoint:
 * $\mathcal R \cap \mathcal R^{-1} = \varnothing$

Also see

 * Equivalence of Definitions of Asymmetric Relation