# Definition:Trivial Relation

## 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 $T$:

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

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.

## Sources

- 1960: Paul R. Halmos:
*Naive Set Theory*... (previous) ... (next): $\S 7$: Relations