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    tlana's Avatar
    tlana Posts: 5, Reputation: 1
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    #1

    Sep 9, 2012, 07:55 AM
    Finite Math help for free?
    A and B are subsets of the universal set U. Given n(A')=23, n(B')=16, and n((A ∩ B) U (AUB)'))= 24, find (A∩B)

    I know the answer, I just don't know how to get it without guessing and checking.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Sep 9, 2012, 08:14 AM
    What does (A ∩ B) mean?
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    tlana Posts: 5, Reputation: 1
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    #3

    Sep 9, 2012, 08:26 AM
    Sorry, n(A ∩ B)
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    #4

    Sep 9, 2012, 08:27 AM
    Um... yea, but I was trying to know if you really understand what each of the terms in "n((A ∩ B) U (A U B)')) = 24" mean.
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    tlana Posts: 5, Reputation: 1
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    #5

    Sep 9, 2012, 09:05 AM
    Quote Originally Posted by Unknown008 View Post
    Um... yea, but I was trying to know if you really understand what each of the terms in "n((A ∩ B) U (A U B)')) = 24" mean.
    The number of elements in the intersection of A and B or Not in A nor B is 24.
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    #6

    Sep 9, 2012, 09:06 AM
    Can you draw this on a Venn diagram, and on separate diagrams, the other information provided?
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    tlana Posts: 5, Reputation: 1
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    #7

    Sep 9, 2012, 09:23 AM
    Quote Originally Posted by Unknown008 View Post
    Can you draw this on a Venn diagram, and on separate diagrams, the other information provided?
    The space (sometimes an oval) between A and B would be counted (or shaded), and the area outside of A and B would be shaded. I can't post pictures online because I don't have a camera or scanner connected to my desktop.
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    Unknown008 Posts: 8,076, Reputation: 723
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    #8

    Sep 9, 2012, 10:11 AM


    1. n((A ∩ B) U (A U B)')) = 24
    2. n(A') = 23
    3. n(B') = 16

    Okay, can you try to do a relation about those?
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    tlana Posts: 5, Reputation: 1
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    #9

    Sep 9, 2012, 10:37 AM
    Quote Originally Posted by Unknown008 View Post


    1. n((A ∩ B) U (A U B)')) = 24
    2. n(A') = 23
    3. n(B') = 16

    Okay, can you try to do a relation about those?
    Initially I was going to say that n((A ∩ B) U (A U B)'))-n(B')-n(A')=(A ∩ B), but that doesn't work, since it's negative and I'm subtracting the area outside A and B twice. Since I was able to guess and check the answer, I know that the sum of n(A') and n(B') minus n((A ∩ B) U (A U B)')) is what is outside of A and B. However, I'm sure that's just luck.

    Short answer: No, I can't...
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    Unknown008 Posts: 8,076, Reputation: 723
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    #10

    Sep 9, 2012, 11:27 AM
    Hmm, I think the easiest way for me would be to assign some variables to the different areas.

    n((A U B)') = a
    n(A ∩ B) = b
    n(A ∩ B') = c
    n(A' ∩ B) = d

    The first picture says: a + b = 24
    The second: a + d = 23
    The third: a + c = 16

    And you are asked to find b.

    Well, I don't think that there is a single solution to this.

    For instance, we can get:
    b - d = 1
    b - c = 8
    d - c = 7

    And get that:
    8 < b <= 24
    7 < d <= 23
    0 <= a < 16

    Taking b = 9:
    a = 15
    c = 1
    d = 8

    Taking b = 10;
    a = 14
    c = 2
    d = 9

    [... ]

    Taking b = 24;
    a = 0
    c = 16
    d = 23

    Which are all valid possibilities.

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