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Math Help - set theory help please

  1. #1
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    set theory help please

    I posted this elsewhere and just realized it was in the wrong place so sorry about that. Heres my problem:


    I know total number of elements in set A, the total number of elements in set B, and the total number of elements in set C. I also know the number of elements in A intersects B, A intersects C, B intersects C, and I know the number of elements that are not in A, B, or C. How do I find:

    1. The number of elements in A intersects B intersects C, and;
    2. The number of elements exclusive to set A, set B, and set C?

    Thanks in advance for your help!

    I posted this before, since then I figured out A intersects b intersects c(I used Aunion B union c = A +b + C - A intersect B -A intersect C - B intersect C + A intersect B intersect C and just plugged in all the numbers).

    But I need to complete a venn diagram and I'm not sure how to find the elements exclusive to each set. I tried to do B - B intersect A - B intersect C - B intersect A intersect C for each section but when I added up my totals it did not add to the desired amount.

    Assignment is due today so any help is appreciated.
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  2. #2
    MHF Contributor

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    This is the set of elements exclusive to A: A \cap B^c  \cap C^c  = A\backslash \left( {B \cup C} \right).
    \left| {A \cap B^c  \cap C^c } \right| = \left| A \right| - \left| {A \cap B} \right| - \left| {A \cap C} \right| + \left| {A \cap B \cap C} \right|
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