Definition:Null Relation

The empty set $$\mathcal{R} = \varnothing$$ is a relation in $$S$$ to $$T$$ such that no element of $$S$$ relates to any element in $$T$$:

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

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