# Definition:Null Relation

(Redirected from Definition:Empty Relation)

## Definition

The null relation is a relation $\mathcal R$ in $S$ to $T$ such that $\mathcal R$ is the empty set:

$\mathcal R \subseteq S \times T: \mathcal R = \O$

That is, no element of $S$ relates to any element in $T$:

$\mathcal R: S \times T: \forall \tuple {s, t} \in S \times T: \neg s \mathrel {\mathcal R} t$

## 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.

## Also see

• Results about the null relation can be found here.