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Math Help - Prove or find counterexamples

  1. #1
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    Prove or find counterexamples

    If A x B = empty set then A = empty set or B = empty set.
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    Senior Member vincisonfire's Avatar
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    What is the "x"?
    Is it intersection? union?
    Are A and B groups, sets, rings?
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  3. #3
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    Quote Originally Posted by vincisonfire View Post
    What is the "x"?
    Is it intersection? union?
    Are A and B groups, sets, rings?
    the x stands for multiplication.

    If A multiply B = empty set then A = empty set or B = empty set.

    or - stands for Union but in this question i don't think the "or" means Union in this question though.
    although that's actually a very good question! hmmm..
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  4. #4
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    Quote Originally Posted by mbcsantin View Post
    the x stands for multiplication.
    Quote Originally Posted by mbcsantin View Post
    If A multiply B = empty set then A = empty set or B = empty set.
    No it does not stand for multiplication in a set theoretic context.
    It is a cross product: A \times B = \left\{ {\left( {a,b} \right):a \in A\,\& \,b \in B} \right\}.
    Now it is perfectly clear that if either set is empty then the cross product is empty and visa versa.
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