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Math Help - Mathematical relations.....

  1. #1
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    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?
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  2. #2
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    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.
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