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Don't know where to start with this one

  1. Feb 3, 2004 #1
    How do I start a problem like this? I need to prove it's true or provide a counterexample if it is false.

    A \ (B union C) = (A \ B) union (A \ C)

    If someone could point me in the right direction, then I would appreciate it.
  2. jcsd
  3. Feb 4, 2004 #2
    i would start with a venn diagram. three circles: one for A, one for B, and one for C. then shade in A \ (B union C) and draw a separate diagram and shade in (A \ B) union (A \ C). if the two shaded regions are identical, then try to prove it's true. if they're not identical, that will narrow your search for a counterexample.
  4. Feb 4, 2004 #3

    matt grime

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    you could just prove it:

    x in A\(BuC) iff (x in A) and (x not in (BuC) iff etc...

    Of course we could pass to a universe, X\Y = X intersect Y^c, and the question just needs you to know about interesections.
  5. Feb 11, 2004 #4
    I'm not too familiar with this, but if we take a numeric example, then does 'union' act as the addition operator? Can we perform arithmetic operations on sets?

    For example, take A={3}, B={2}, C={5}

    Then would

    A /(B u C) = 3 / (2+5) = 3/7


    (A/B) u (A/C) = (3/2) + (3/5) = 21/10

    thus providing a counterexample?

    Please correct me if I'm wrong.
    Last edited: Feb 11, 2004
  6. Feb 12, 2004 #5
    Yes, in some sense, but it's hardly defined exactly like the "normal" addition operator... See Wikipedia, set theory for more info.

    In your example, B union C = {2, 5}, not 7!

    Also, \ stands for complement, not division.
    Last edited: Feb 12, 2004
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