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Math Help - Counting Sets

  1. #1
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    Counting Sets

    Let A and B be sets in a universe,
    with |A ∩ B| = 4
    |A U B| = 7
    Determine the number of subsets in A U B which contains A ∩ B.

    My Solution:
    |AUB| = |A| + |B| - |A∩B|
    =3+4-4=3

    |A∩B|=|A|+|B|-|AUB|
    =3+4-3=4

    4+3=7

    However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

    Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks
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  2. #2
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    Quote Originally Posted by hugo84 View Post
    Let A and B be sets in a universe,
    with |A ∩ B| = 4
    |A U B| = 7
    Determine the number of subsets in A U B which contains A ∩ B.

    My Solution:
    |AUB| = |A| + |B| - |A∩B|
    =3+4-4=3

    |A∩B|=|A|+|B|-|AUB|
    =3+4-3=4

    4+3=7

    However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

    Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks
    The numbers are pretty small, and one way to approach this problem is simply to make two sets A and B that fit the description and see what you have.

    A={1,2,3,4}
    B={1,2,3,4,5,6,7}

    In this case A U B = B, but the lack of generality won't make the result invalid.

    How many subsets of B contain A?

    So the elements 5, 6, and 7, each can either be or not be in the subset. That is 2^3 possibilities. So I think the answer is 8.
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  3. #3
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    Quote Originally Posted by hugo84 View Post
    Let A and B be sets in a universe,
    with |A ∩ B| = 4
    |A U B| = 7
    Determine the number of subsets in A U B which contains A ∩ B.

    My Solution:
    |AUB| = |A| + |B| - |A∩B|
    =3+4-4=3

    |A∩B|=|A|+|B|-|AUB|
    =3+4-3=4

    4+3=7

    However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

    Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks
    Fear you have not understood the question well. Where are you given |A| and |B| that you have used?
    Let me ask a similar (infact exactly same question). You are given a set of 7 elements.
    1. How many subsets this set has?
    2. How many subsets are there that contain 4 particular elements?

    Can you ans the above?
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  4. #4
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    thanks for the clarification, understood
    To: aman_cc
    Qn1:2^7
    Qn2:2^4
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