Definition:Trivial Relation

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Definition

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 $T$:

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


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.


Sources