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Math Help - Function

  1. #1
    Super Member Showcase_22's Avatar
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    Function

    List all functions from \{a,b\} to \{1,2\}.

    For some reason I keep missing one!! I know that I should have 2^2 functions.

    So I start by mapping a to 1 and 2, leaving b alone.

    Then I map b to 1 and 2, leaving a alone.

    Then I map a to 1, and b to 2.

    But i'm missing one!

    Is it a null function? One that doesn't map a and b to anything?
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  2. #2
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    \left\{ {(a,1),(b,1)} \right\},~\left\{ {(a,1),(b,2)} \right\},~\left\{ {(a,2),(b,1)} \right\},~\&~\left\{ {(a,2),(b,2)} \right\}<br />
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  3. #3
    MHF Contributor

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    Quote Originally Posted by Showcase_22 View Post
    List all functions from \{a,b\} to \{1,2\}.

    For some reason I keep missing one!! I know that I should have 2^2 functions.

    So I start by mapping a to 1 and 2, leaving b alone.

    Then I map b to 1 and 2, leaving a alone.
    Neither of those are functions!

    Then I map a to 1, and b to 2.

    But i'm missing one!

    Is it a null function? One that doesn't map a and b to anything?
    I think you need to review the definition of "function".

    1\to a, 2\to a
    1\to b, 2\to b
    1\to a, 2\to b
    1\to b, 2\to a

    Plato did it to me again- got his response in while I was still typing mine!
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