Definition:Antisymmetric Relation/Definition 2

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

Also known as
Some sources render this concept as anti-symmetric relation.

Some sources (perhaps erroneously) use this definition for an asymmetric relation.

Also see

 * Equivalence of Definitions of Antisymmetric Relation


 * Definition:Symmetry (Relation)


 * Definition:Symmetric Relation
 * Definition:Asymmetric Relation
 * Definition:Non-symmetric Relation