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List all the functions from the three-element set

  1. Sep 14, 2008 #1
    Dear all,

    List all the functions from the three-element set {1,2,3} to the set {a,b}.

    The answer I have is 6 functions. However, the answer given at the back of the book has 24 functions:

    Note: In the following functions, I will use (sub 1) denoting subscript 1.



    f (sub 1) (1)=a , f (sub 1) (2)=a , f (sub 1) (3)=a
    f (sub 2) (1)=a , f (sub 2) (2)=a , f (sub 2) (3)=b
    f (sub 3) (1)=a , f (sub 3) (1)=b , f (sub 1) (1)=a
    f (sub 4) (1)=a , f (sub 4) (1)=b , f (sub 4) (1)=b
    f (sub 5) (1)=b , f (sub 5) (1)=a , f (sub 5) (1)=a
    f (sub 6) (1)=b , f (sub 6) (1)=a , f (sub 6) (1)=b
    f (sub 7) (1)=b , f (sub 7) (1)=b , f (sub 4) (1)=a
    f (sub 8) (1)=b , f (sub 8) (1)=b , f (sub 8) (1)=b
     
  2. jcsd
  3. Sep 16, 2008 #2
    Re: Functions (urgent)

    I think I did not make myself clear in the above thread.

    I would like to know why are there 8 functions?
     
  4. Sep 16, 2008 #3

    Dick

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    Science Advisor
    Homework Helper

    Re: Functions (urgent)

    There are 8 functions. 8=2^3. If the book says there are 24, it's quite wrong.
     
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