# Definition:Relation/Truth Set

## Definition

Let $S \times T$ be the cartesian product of two sets $S$ and $T$.

Let $\RR$ be a relation on $S \times T$.

The truth set of $\RR$ is the set of all ordered pairs $\tuple {s, t}$ of $S \times T$ such that $s \mathrel \RR t$:

$\map \TT \RR = \set {\tuple {s, t}: s \mathrel \RR t}$

## Also known as

The truth set of a relation is sometimes seen referred to as its graph.

However, this term is most usually seen in the context of a mapping.