Mathematical relations.....

Quote:

Originally Posted by Colette

Hi folks can anyone answer this for me Plz..
Let R and S be relations on a set X.Show that R x S is a relation on X x X?

You know that,
$R\subseteq (X\times X)$ (1)
$S\subseteq (X\times X)$ (2)
Any element of,
$R\times S$ is $((r_1,r_2),(s_1,s_2))$ where $r_1,r_2,s_1,s_2 \in X$ by (1) and (2). Thus, $((r_1,r_2),(s_1,s_2))\in (X\times X)^2$ . Thus, you shown that this direct product is a subset and the proof is complete.