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Finite Product Sets

  1. May 30, 2005 #1
    I have to find an example illustrating the the equation
    (A x B) U (X x Y) = (A U X) x (B U Y) is not valid for all choices of sets A,B,X,Y.

    I started out by saying that

    let (x,y) be in A and B or
    let (x,y) be in X and Y

    Since x is in A and y is in B
    --> (x,y) = (A x B)
    Since x is in X and y is in Y
    --> (x,y) = (X x Y)

    Can I go on to say that since x is in A and x is in A
    x is a subset of (A U X)?

    How do I prove that this is not true?
  2. jcsd
  3. May 30, 2005 #2
    You're thinking much too hard. Pick A, B, X, Y as singletons, etc.
  4. May 31, 2005 #3
    (A U X) x (B U Y) can never be of prime cardinality if A U X and B U Y are not singletons.

    When can (A x B) U (X x Y) be of prime cardinality?
  5. Jun 1, 2005 #4
    Is it when it's an intersection? Okay, so I will have to find a counterexample for it. Also, I was wondering if it's wise to start off by trying to prove the example, and then find out that its wrong, and then to find a counterexample for it.
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