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Which functions am I missing?

  1. Feb 21, 2016 #1
    1. The problem statement, all variables and given/known data
    How many functions are there from {1,2,3} to {a,b}? Which are injective? Which are surjective?

    2. Relevant equations
    n^m. gives the number of functions

    3. The attempt at a solution
    To me the number of functions that can be made are 6 because 3x2=6 but I have read online that n^m, n being the elements in the second set and m being the number of elements in the first set, gives you the number of functions. That equation gives me 8 functions but for the life of me I can't figure which functions I'm leaving out.
    20160221_200842.jpg
    Also there can't be any injective functions because f(1) can take 2 values and f(2) can take one value. Leaving f(3) with none so therefore It can't be injective,correct?
     
  2. jcsd
  3. Feb 21, 2016 #2

    SammyS

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    You are missing two functions for which 1 → b .
     
  4. Feb 21, 2016 #3
    Thank you, was my explanation for injective correct?
     
  5. Feb 21, 2016 #4

    SammyS

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    Yes
     
  6. Feb 21, 2016 #5
    Awesome thank you :)
     
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