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Math Help - set theory

  1. #1
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    set theory

    A salesman visits 274 housewifes in a town to find out their views about three products A,B and C. He finds that
    157 use A,
    9 use all three,
    14 use A and C but not B,
    39 use B and C,
    48 use only B

    (i) Which product is most popular according to this enquiry.
    (ii) How many use product C only.

    Please solve the problem and explain the steps.
    thanks
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  2. #2
    Senior Member vincisonfire's Avatar
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    It seems one information is missing to solve number a).
    Do a Venn diagram.
    You will find
     9 \in A \cap B \cap C *
     14 \in A \cap C \setminus B
     39 \in B \cap C
    You know that  9 \in A \cap B \cap C so you can deduce
     30 \in B \cap C \setminus A
     48 \in B \setminus (A \cup B)
    You know that  157 \in A so
     144 \in (A \setminus (B \cup C)) \cup (A \cap B)\setminus (A\cap B\cap C)
    Finally  29 \in C \setminus A \cup B
    Last edited by vincisonfire; January 5th 2009 at 06:25 PM.
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