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Math Help - More set theory trouble

  1. #1
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    More set theory trouble

    Ok so say the cardinality of.....

    U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17



    How do I find |ABC|

    note:all adjacent sets are intersect. This completely vexes me.
    Last edited by ehpoc; November 26th 2011 at 02:32 PM.
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    Re: More set theory trouble

    Quote Originally Posted by ehpoc View Post
    Ok so say the cardinality of.....
    U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17
    How do I find |ABC|
    note:all adjacent sets are intersect. This completely vexes me.
    [TEX]A\cap B~\&~A\cup B[/TEX] gives A\cap B~\&~A\cup B.

    From that given all you can say is |ABC|\le \min\{|AB|,|AC|,|BC|\}=11
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    Re: More set theory trouble

    I honestly do not understand how we can come to any single conclusion about |ABC|
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    Re: More set theory trouble

    Quote Originally Posted by ehpoc View Post
    I honestly do not understand how we can come to any single conclusion about |ABC|
    No one can. There are twelve different possible values: \{0,1,\cdots,11\}
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    Re: More set theory trouble

    Quote Originally Posted by ehpoc View Post
    Ok so say the cardinality of.....

    U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17

    How do I find |ABC|

    note:all adjacent sets are intersect. This completely vexes me.
    Inclusion
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    Re: More set theory trouble

    So when a question ask "What is |ABC|" it is not really asking that? Why would the question not ask what is the maximum that |ABC| could be?

    So when you say 11 you are saying "there is at most 11 elements in ABC"?

    Oh btw I just realized that I missed out one key premise.... AuBuC=109 I think I can solve it now. I keep getting psyched out by these problems and choking really.

    EDIT: nope still can't solve it. LOL
    Last edited by ehpoc; November 26th 2011 at 02:55 PM.
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    Re: More set theory trouble

    Quote Originally Posted by ehpoc View Post
    So when a question ask "What is |ABC|" it is not really asking that? Why would the question not ask what is the maximum that |ABC| could be?
    Oh btw I just realized that I missed out one key premise.... AuBuC=109 [/QUOTE]
    Now it can be solved.
    109=58+40+46-13-11-17+|ABC|
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  8. #8
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    Re: More set theory trouble

    If you're having trouble visualizing this, a Venn Diagram is just what the doctor ordered. (Particularly with three sets, where all intersections are represented.)
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