Definition:Trivial Relation

Definition
The trivial relation is the relation $$\mathcal R \subseteq S \times T$$ in $$S$$ to $$T$$ such that every element of $$S$$ relates to every element in $$T$$:


 * $$\mathcal R: S \times T: \forall \left({s, t}\right) \in S \times T: \left({s, t}\right) \in \mathcal R$$

That is:
 * $$\mathcal R = S \times T$$

... the relation which equals the product of the sets on which it is defined.