Definition:Serial Relation

Definition

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

$\RR$ is serial if and only if:

$\forall x \in S: \exists y \in S: \tuple {x, y} \in \RR$

That is, a relation $\RR \subseteq S \times S$ is serial if and only if every element of $S$ relates to some other element of $S$.

Also see

• Definition:Left-Total Relation
• Definition:Right-Total Relation

• Results about serial relations can be found here.

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $5$ Properties of Relations: Exercise $2$