Definition 5.41 (Total)

#Definition

A relation $R$ on a set $A$ is called $total$ if all $a, b \in A$ satisfy: $(a, b) \in R$ or $(b, a) \in R$

Tip

This can be formalised in predicate logic by

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

Where the domain is the set of all elements in $A$