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Math Help - Correctness of a sample function

  1. #1
    terencetham
    Guest

    Correctness of a sample function

    function f: {a, b, c} -> {1, 2 ,3} defined by f(a) = 1, f(b) = 1, f(c) = 2

    if ~f(y) represents inverse function

    is ~f({1,3}) = {a, b} correct? or should it be ~f({1}) = {a, b}

    the former is printed in the book and i'm kinda confused why ~f({1, 3}) gives {a,b} since ~f({3}) gives NIL.

    Appreciate any clarification

    Thank you
    Last edited by terencetham; June 25th 2006 at 04:31 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by terencetham
    function f: {a, b, c} -> {1, 2 ,3} defined by f(a) = 1, f(b) = 1, f(c) = 2

    if ~f(y) represents inverse function

    is ~f({1,3}) = {a, b} correct? or should it be ~f({1}) = {a, b}

    the former is printed in the book and i'm kinda confused why ~f({1, 3}) gives {a,b} since ~f({3}) gives NIL.

    Appreciate any clarification

    Thank you
    <br />
f^{-1}(\{1,3\})=f^{-1}(\{1\})\cup f^{-1}(\{3\})=\{a,b\}\cup \emptyset=\{a,b\}<br />

    where \emptyset denotes the empty set, and so for any set A, A \cup \emptyset=A

    RonL
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