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Homework Help: Sets and functions, theoretical calc homework?

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Let A,B, and C be subsets of universal set U. Prove the following
    A. If U=A union B and intersection of A and B is not an empty set, then A= U\B
    B. A\(B intersection C) = (A\B) union (A\C)

    2. Relevant equations

    no relevant equations required

    3. The attempt at a solution
    So I know A union B = {x: (xεA) or (xεB)}
    But I am having trouble on where to go from there. Intuitively I can see that the claim is true, but how do I prove this? step by step please

    I know that B intersection C= : {x: (xεB) and (xεC)}
    A\B = {x: (xεA) and ~(xεB)}
    A\C = {x: (xεA) and ~(xεC)}
    Same problem as part a how do I prove this?
  2. jcsd
  3. Jan 26, 2014 #2


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    Hello concon,

    Welcome to PF !

    We don't do step by step solutions here at PF, if that's what you're asking for.

    It looks to me that A is not true.

    In general, to show that two sets are equal, i.e. D = E, show that D is a subset of E and E is a subset of D.
    To show that set D is a subset of E:
    Let xεD. Then show that it follows that xεE .
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