# Mathematical relations.....

• Aug 11th 2006, 03:18 AM
Colette
Mathematical relations.....
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?
• Aug 11th 2006, 08:54 AM
ThePerfectHacker
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.