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Math Help - Help on a Proof

  1. #1
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    Help on a Proof

    Hi i have the following question about Cartesian Products:

    Prove, or disprove:

    If A × B = A × C, then B = C.
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  2. #2
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    Are you sure it has no restrictions on A?

    If not, then if A=0, then B not necessarily = C. For example, 0*2 = 0*4, 4 not equal 2.
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  3. #3
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    tripod87, he said "Cartesian products". A, B, and C are sets, not numbers.

    However, with slightly different notation, the same objection works! (So it is possible that tripod87 meant that but used numerical notation.) If A is the empty set then A X B and A X C are empty for all B and C.

    Suppose A is not empty. If x is any member of B, there exist a pair (a, x) in A X B for some a in A. Since A X B= A X C, that pair is also in A x C. Therefore x is in C. Then B is a subset of C. Can you finish?
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