Definition:Trivial Relation

Definition

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

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

That is:

$\RR = S \times T$

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
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Relations