Diagonal Relation is Serial

Theorem

Let $S$ be a set.

Let $\Delta_S$ be the diagonal relation on $S$.


Then $\Delta_S$ is a serial relation.


Proof

By Diagonal Relation is Equivalence it follows a fortiori that $\Delta_S$ is reflexive.

The result follows from Reflexive Relation is Serial.

$\blacksquare$


Sources

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