Definition:Relation/Truth Set

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Definition

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

Let $\mathcal R$ be a relation on $S \times T$.


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

$\map {\mathcal T} {\mathcal R} = \set {\tuple {s, t}: s \mathrel {\mathcal R} t}$


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.


Sources