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Math Help - Help with Discrete Maths Question.... stuck :(

  1. #1
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    Help with Discrete Maths Question.... stuck :(

    Code:
    Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Someone gives you six numbers  a1,....,a6 from S.
    Let P = {{x, y} | x, y   S and x + y = 15}
    If f: {a1,...,a6} -> P is defi ned by f(ai) equals the set containing ai, explain
    why f is not one-one.

    If ai != (does not eqaul) aj but f(ai) = f(aj) show that ai + aj = 15.

    Explain why, if 6 numbers are chosen from S then the sum of some pair of them
    is 15.

    Can someone help me

    Cheers
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  2. #2
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    Quote Originally Posted by Privoxy View Post
    Code:
    Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Someone gives you six numbers  a1,....,a6 from S.
    Let P = {{x, y} | x, y   S and x + y = 15}
    If f: {a1,...,a6} -> P is defi ned by f(ai) equals the set containing ai, explain
    why f is not one-one.

    If ai != (does not eqaul) aj but f(ai) = f(aj) show that ai + aj = 15.

    Explain why, if 6 numbers are chosen from S then the sum of some pair of them
    is 15.

    Can someone help me

    Cheers
    Are you having trouble understanding the questions? Mainly it's just definitions, and for the last part the pidgeonhole principle.
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  3. #3
    MHF Contributor
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    For starters, I would recommend writing out the set P explicitly. Also, one has to understand why
    f: \{a_1,...,a_6\}\to P is defi ned by f(a_i) equals the set containing \displaystyle a_i
    is a correct definition of a function. By this I mean why for any a_i there exists an (unordered) pair p from P such that a_i\in p and why such p is unique.
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