Definition 5.38.1 (Symmetric)

#Definition

A relation $R$ on a set $A$ is called $symmetric$ , if $(a, b) \in R$ implies $(b, a) \in R$ for all $a, b \in A$

Tip

Symmetric can be formalised in predicate logic by

\forall x \forall y ((x, y) \in R \to (y, x) \in R)

Here, the domain is the set of all elements is $A$