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Set theory proof homework

  1. Jul 7, 2009 #1
    1. The problem statement, all variables and given/known data

    1)Prove for all sets A and B contained in a universe U, if A intersection B' = nullspace then
    P(A) − P(B) is a subset of P(A − B).

    2)Prove for all sets A and B contained in a universe U, if A intersection B = nullspace then
    P(A) − P(B) is a subset of P(A − B).

    3)Prove for all sets A and B contained in a universe U, if A intersection B' = nullspace and
    A intersection B = nullspace, then P(A) − P(B) is not a subset of P(A − B).

    2. Relevant equations

    I've trired some. I just need to know if the first one is correct. I don't know how to do the other 2. Please help me asap. Thanks.

    3. The attempt at a solution

    1) A inter B = nullspace...Hence A inter B is a subset of nullspace and nullspace is a subset of A inter B.
    Hence nullspace is a subset of A and is a subset of B'-----(a)
    Hence nullspace belongs to P(A) and also to P(B')
    Hence nullspace belongs to P(A)-P(B).
    From (a) we have nullspace is a subset of A and is not a subset of B
    Hence nullspace is a subset of (A-B)
    Hence nullspace belongs to P(A-B)
    therefore P(A)-P(B) is a subset of P(A-B)
     
  2. jcsd
  3. Jul 8, 2009 #2
    This is invalid: Hence nullspace belongs to P(A)-P(B).

    Things you stated up to that point are true, but mostly not of much use, since the nullset is automatically a subset of any set (in particular of A and B and B' and...)
     
  4. Jul 8, 2009 #3
    So what do you suggest i do?
     
  5. Jul 8, 2009 #4
    Review the definitions of the items in the statement of the problem.
     
  6. Jul 8, 2009 #5
    how about i do this:

    let x belong to P(A)-P(B)
    so x is a subset of A and is not a subset of B
    so x is a subset of (A-B)
    so x belongs to P(A-B)
    hence P(A)-P(B) is a subset of P(A-B)
     
  7. Jul 8, 2009 #6
    someone please help
     
  8. Jul 9, 2009 #7
    a good start

    does not follow
     
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