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(A - B) union (B- A) = (A union B) - (A intersection B)

  1. Jun 27, 2009 #1
    Why is this true: (A - B) union (B- A) = (A union B) - (A intersection B)

    wouldn't the union of A and B everything that is in A or B? And since A - B and B - A don't contain any elements from the other set, wouldn't the union of these be equal to union of A and B?

    So wouldn't it make sense for it to be: (A - B) union (B- A) = (A union B)?

    I don't think that A union B contains elements in A or B AND A and B.
  2. jcsd
  3. Jun 27, 2009 #2
    Last edited by a moderator: May 4, 2017
  4. Jun 27, 2009 #3
    Re: Union/Intersection

    For an intuitive expalanation consider the Venn diagram here.

    This doesn't hold for A={1,2} and B={2,3}.
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