Definition:Trivial Relation

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The trivial relation is the relation $\mathcal R \subseteq S \times T$ in $S$ to $T$ such that every element of $S$ relates to every element in $T$:

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

That is:

$\mathcal R = S \times T$

the relation which equals the product of the sets on which it is defined.

Also see

  • Results about the trivial relation can be found here.