# Thread: Quick function problem

1. ## 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

2. 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?

3. 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)

4. Originally Posted by zhupolongjoe
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 $\displaystyle n^m$ functions from A to B