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Math Help - Question on counting finite sets.

  1. #1
    Newbie Doktor_Faustus's Avatar
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    Question on counting finite sets.

    Of the 32 people who save paper N(P) or bottles N(B) ( or both ) for recycling, 30 save paper and 14 save bottles. Find the number m, of people who

    (a) save both
    (b) save only paper
    (c) save only bottles


    in (a) m = N (P n B ) = N(p) + N(B) - N (P u B)

    My understanding is that the intersection of P and B is those people who save paper and bottles. Ok easy enough, but when I read the equation above I read it like this : "The number of people who save paper and bottles equals the number of people who save paper only plus the number of people who save bottles only minus the number of people who save paper, or save bottles, or save both." In this case P u B = the universe. So subtracting people who do one thing or the other from this will leave you with people who do both. Am I understanding this correctly ?

    in (b) m= N (P\B) = N(P) - N ( P n B). So, the number of people who save paper only ( set difference of P and B ) equals the number of people who save paper only minus the number of people who save paper and bottles. What about the people who save bottles only ? Surely they must be subtracted aswell ?

    The answers I've given are taken from the notes I'm reading, so I'm assuming they're correct.

    Anyone care to show me the light ?
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  2. #2
    Super Member
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    You got a few things mixed up. Please read my comments in line carefully

    Quote Originally Posted by Doktor_Faustus View Post
    Of the 32 people who save paper N(P) or bottles N(B) ( or both ) for recycling, 30 save paper and 14 save bottles. Find the number m, of people who

    (a) save both
    (b) save only paper
    (c) save only bottles


    in (a) m = N (P n B ) = N(p) + N(B) - N (P u B)

    My understanding is that the intersection of P and B is those people who save paper and bottles. Ok easy enough, but when I read the equation above I read it like this : "The number of people who save paper and bottles equals the number of people who save paper only plus the number of people who save bottles only minus the number of people who save paper, or save bottles, or save both." In this case P u B = the universe. So subtracting people who do one thing or the other from this will leave you with people who do both. Am I understanding this correctly ?

    "The number of people who save paper and bottles (i.e. save both) equals the number of people who save paper plus the number of people who save bottles minus the number of people who save paper only, or save bottles only, or save both."

    in (b) m= N (P\B) = N(P) - N ( P n B). So, the number of people who save paper only ( set difference of P and B ) equals the number of people who save paper only minus the number of people who save paper and bottles. What about the people who save bottles only ? Surely they must be subtracted aswell ?

    "So, the number of people who save paper only ( set difference of P and B ) equals the number of people who save paper minus the number of people who save paper and bottles (both)."

    The answers I've given are taken from the notes I'm reading, so I'm assuming they're correct.

    Anyone care to show me the light ?
    Follow Math Help Forum on Facebook and Google+

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