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Homework Help: Complementary sets

  1. Jan 10, 2013 #1
    1. The problem statement, all variables and given/known data

    If n(A - B) = 5, n(A' - B) = 4, n(A') = 10, n(B'-A') = 12. What is n(AUB) = ?

    2. Relevant equations

    3. The attempt at a solution
    I drew a big rectangle and inside 2 intersected diagrams A and B. I drew 5 dots in the (( of diagram A. Now that A' is complementary that means they have nothing in common, so I drew 5 dots outside of the diagrams(inside the rectangle).
    n(B' - A') = 12. If A' = 10. B' = 2?

    About the question above. NOTHING else is given, just that.
  2. jcsd
  3. Jan 10, 2013 #2


    Staff: Mentor

    so start with the venn diagram and put in the numbers you know and for (A intersection B) put in an X and try to use your logic to figure out the counts for the four areas and then the A union B should be obvious.
  4. Jan 10, 2013 #3


    Staff: Mentor

    You're assuming that the two sets intersect, which might not be true, based on the given information.

    I think there are four possibilities:
    1) A and B are disjoint (no common members)
    2) A and B intersect for some members, but not all of them (i.e., some members of A aren't also in B, and vice versa)
    3) A is completely contained in B
    4) B is completely contained in A

    Draw a Venn diagram for each of these scenarios. For each one identify the sets A - B, A' - B, A', and B' - A'. See if you can sprinkle your dots so that the four given conditions are met. You should then be able to determine n(A U B).
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