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