Definition:Right-Total Relation

From ProofWiki
Jump to navigation Jump to search


Let $S$ and $T$ be sets.

Let $\RR \subseteq S \times T$ be a relation in $S$ to $T$.

Then $\RR$ is right-total if and only if:

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

That is, if and only if every element of $T$ is related to by some element of $S$.

That is, if and only if:

$\Img \RR = T$

where $\Img \RR$ denotes the image of $\RR$.

Also known as

A right-total relation can also be referred to as surjective or onto.

Also see