Definition:Symmetric Relation/Definition 3

Definition

Let $\RR \subseteq S \times S$ be a relation in $S$.

$\RR$ is symmetric if and only if it is a subset of its inverse:

$\RR \subseteq \RR^{-1}$

Also see

• Equivalence of Definitions of Symmetric Relation

• Results about symmetric relation can be found here.

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 10$: Inverses and Composites