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Math Help - One-to-One Function Problem

  1. #1
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    One-to-One Function Problem

    Let A = {1,2,3}

    (a) How many one-to-one functions are there from A to A?
    (b) List all one-to-one functions onto A?

    So far I have this:
    (a) I believe the answer is 6, NOT SURE.

    (b)
    f1: A A
    1 to 1
    2 to 2
    3 to 3

    f2: A A
    1 to 2
    2 to 3
    3 to 1

    f3: A A
    1 to 3
    2 to 1
    3 to 2

    NOT SURE IF I ANM RIGHT? ANY HELP WOULD BE GREAT. THANK YOU!
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  2. #2
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    Your answer of 6 is correct!
    Then why do you just list 3?
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  3. #3
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    Hi Plato,

    I only listed three because that is all I could find. To me I have mapped each to one of the others one time and I don't see any more combinations. I know there should be three more, but I don't know what they would be? Thanks.
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  4. #4
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    Here is a hint: 3!=6.
    abc
    acb
    bac
    bca
    cab
    cba
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  5. #5
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    Quote Originally Posted by Plato View Post
    Here is a hint: 3!=6.
    abc
    acb
    bac
    bca
    cab
    cba
    I see what you mean. I am not sure how I would represent that like the other three functions above?
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  6. #6
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    Quote Originally Posted by Plato View Post
    Here is a hint: 3!=6.
    abc
    acb
    bac
    bca
    cab
    cba
    I see what you mean. I am not sure how I would represent that like the other three functions above in just two columns?
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  7. #7
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    I got it! the other three are:

    f4:
    A A
    1 to 1
    2 to 3
    3 to 2


    f5:
    A A
    1 to 3
    2 to 2
    3 to 1

    f6:
    A A
    1 to 2
    2 to 1
    3 to 3
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by MathStudent1 View Post
    I got it! the other three are:

    f4:
    A A
    1 to 1
    2 to 3
    3 to 2


    f5:
    A A
    1 to 3
    2 to 2
    3 to 1

    f6:
    A A
    1 to 2
    2 to 1
    3 to 3
    Bravo! or is it brava? not sure if you're a guy or girl
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