Definition:Symmetric Relation

Definition
Let $\mathcal R \subseteq S \times S$ be a relation in $S$. $\mathcal R$ is symmetric iff:


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

Also see

 * Definition:Symmetry (Relation)


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