User:Ascii/Prose Test/Relation Theory

Images

Let $\mathcal R \subseteq S \times T$ be a relation.

Let $A, B \subseteq S$.

The image of an element $x$ of $S$ is equal to the image of a singleton of $x$: $\forall x \in S: \map \RR x = \RR \sqbrk {\set x}$

If $A$ is a subset of $B$ then the image of $A$ is a subset of the image of $B$: $A \subseteq B \implies \RR \sqbrk A \subseteq \RR \sqbrk B$