Definition:Null Relation

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.