Problem Statement:
Let $A$ and $B$ be sets. Many books define a relation $\mathcal R$ from $A$ to $B$ to be a subset $ \mathcal R \subseteq A \times B $.
Show that such an R is a relation on A∪B according to the following definition :
Definition:
A relation $\mathcal R $ on a set $S$ is a collection of ordered pairs of elements of $S$; that is, a subset $ \mathcal R \subseteq S \times S$.
The assertion $(x, y) \in \mathcal R$ is usually abbreviated $x \mathcal Ry$, and we say $x$ is related to $y$ by $ \mathcal R.$ If $(x, y) \notin \mathcal R$
we write $ x \not \mathcal R y$.
How would approach this problem? I don't quite understand how to. It seems rather ambiguous and obvious
Let $S = A \cup B$, let $\mathcal{R} \subseteq A \times B$, and let $(x,y) \in \mathcal{R}$. Then $x \in A \subseteq S$ and $y \in B \subseteq S$, so $(x,y) \in S \times S$. Therefore $\mathcal{R} \subseteq S \times S$.
(At least, I think that's what's being asked...)