Antisymmetric Relation

Definition

Anti-Symmetry

A relation $R\subseteq A\times B$ is antisymmetric if whenever an element $a\in A$ is in relation with an element $b\in B$ and vice versa, then $a=b$.

$$\forall a\in A:\forall b\in B:aRb\wedge bRa⟹a=b$$