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 $x$: $\forall x \in S: \mathcal R \left({x}\right) = \mathcal R \left[{\left\{{x}\right\}}\right]$

If $A$ is a subset of $B$ then the image of $A$ is a subset of the image of $B$: $A \subseteq B \implies \mathcal R \left[{A}\right] \subseteq \mathcal R \left[{B}\right]$