Definition:Null Relation

Definition
The null relation  is a relation $$\mathcal R$$ in $$S$$ to $$T$$ such that $$\mathcal R$$ is the empty set:
 * $$\mathcal R \subseteq S \times T: \mathcal R = \varnothing$$

That is, no element of $$S$$ relates to any element in $$T$$:
 * $$\mathcal R: S \times T: \forall \left({s, t}\right) \in S \times T: \neg s \, \mathcal R \, t$$

This is also sometimes referred to as a trivial relation by some authors, but to save confusion it's better to use that term specifically to mean this one.