Trivial Question : Union of Relation

Question

$ A,B $ are sets. Let Relation $ R \subseteq A \times A. \; $ Relation $ S \subseteq B \times B $. Can we have $ R \cup S $ ? where the underlying sets are different and if so, what is the underlying set of the union ?

Answer 1

$R\subseteq A\times A$, and $S\subseteq B\times B$, so

$$R\cup S\subseteq (A\times A)\cup(B\times B)\subseteq(A\cup B)\times(A\cup B)\;;$$

$R\cup S$ is a relation on $A\cup B$.