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

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

Other sources prefer to call it the empty relation.