Definition:Symmetric Relation/Definition 1

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


 * $\tuple {x, y} \in \mathcal R \implies \tuple {y, x} \in \mathcal R$

Also see

 * Equivalence of Definitions of Symmetric Relation