Let $A$ be a set.
- The set of symmetric relations on $A$ is the subset $\smash {\mathrm{Rel}^{\mathrm{symm}}\webleft (A,A\webright )}$ of $\mathrm{Rel}\webleft (A,A\webright )$ spanned by the symmetric relations.
- The poset of relations on $A$ is is the subposet $\smash {\mathbf{Rel}^{\mathsf{symm}}\webleft (A,A\webright )}$ of $\mathbf{Rel}\webleft (A,A\webright )$ spanned by the symmetric relations.
