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?

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- Aug 11th 2006, 02:18 AMColetteMathematical 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, 07:54 AMThePerfectHackerQuote:

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.