Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    whereas

    (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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Don't know where to start with this one
  1. Where do I start? (Replies: 5)

  2. Where to start? (Replies: 5)

  3. Where to Start? (Replies: 2)

Loading...