Let S be set of real numbers which is closed under multiplication(that is,if a and b are in S,then so is ab).Let T and U be disjoint subsets of S whose union is S.Given that the product of any three(not necessarily distinct)elements in T is in T and that the product of any three elements of U is in U,show that at least one of the two subsets T, U is closed under multiplication. Is there any one can help me ?

Question

Let S be set of real numbers which is closed under multiplication(that is,if a and b are in S,then so is ab).Let T and U be disjoint subsets of S whose union is S.Given that the product of any three(not necessarily distinct)elements in T is in T and that the product of any three elements of U is in U,show that at least one of the two subsets T, U is closed under multiplication.         Is there any one can help me ?

bahrom7893 · Answer

Okay, let's try this.. I have a feeling this is proof by contradiction..

bahrom7893 · Answer

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