Set of Relations can be Ordered by Subset Relation

Theorem
Let $S \times T$ be the product of two sets.

Let $\mathcal R$ be a set of relations on $S \times T$.

Then $\mathcal R$ can be ordered by inclusion.

Proof
By the definition of relation, any relation $R$ is associated with a subset $R \subseteq S \times T$.

Thus $\mathcal R$ is a subset of the power set $\mathcal P\left({S \times T}\right)$.

The result follows from Subset Relation is Ordering.

Also see

 * Set of Mappings can be Ordered by Inclusion