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Math Help - Quick function problem

  1. #1
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    Quick function problem

    Suppose that set A has m elements and set B has n elements. We have seen that AxB has mn elements and that there are 2^(mn) relations from A to B. Find the number of relations from A to B that are functions from A to B
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  2. #2
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    Hint: What is the difference between a "relation" and a "function"? What restriction does this put on the number of relations that could be functions?
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  3. #3
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    A function is a relation such that there if (x,y)belongs to f and (x,z) belongs to f, then y=z, so perhaps it will be something like -(2^(mn)-mn) since that is like the relations minus the functions, but then the opposite...obviously I can look up basic definitions, that is not where I need help, but thanks anyways.


    EDIT: ignore that, I think it is n^(m)
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  4. #4
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    Quote Originally Posted by zhupolongjoe View Post
    Suppose that set A has m elements and set B has n elements. We have seen that AxB has mn elements and that there are 2^(mn) relations from A to B. Find the number of relations from A to B that are functions from A to B
    For each element of A there n choices from B to pair with it. Thus n^m functions from A to B
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