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Math Help - Let A,B, and C be sets with A not equal to the empty set. If AXB=AXC, then B=C.

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    Let A,B, and C be sets with A not equal to the empty set. If AXB=AXC, then B=C.

    Let A,B, and C be sets where A is not equal to the empty set. If AXB = AXC, then B=C.

    Assume: AxB=AxC

    Prove: B=C

    Explain where the assumption that A is not equal to the empty set is needed, in the proof.

    I know that I must show that B is a subset of C, and C is a subset of B, therefore sense they are subsets of each other they are equal. But I am not sure at all how to show that they are subsets of each other other than basic assumptions. Any help?
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    Re: Let A,B, and C be sets with A not equal to the empty set. If AXB=AXC, then B=C.

    Quote Originally Posted by Brjakewa View Post
    Let A,B, and C be sets where A is not equal to the empty set. If AXB = AXC, then B=C.
    Assume: AxB=AxC Prove: B=C
    Start off with the fact that \left( {\exists a \in A} \right) why is that true?
    If b\in B then (a,b)\in A\times B, WHY?

    Thus b\in C, WHY?

    Now you finish.

    If you cannot, then you need a sit-down with a live tutor.
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