**Let A and B be 2 finite sets having m and n elements respectively ,then the total no of mappings from A to B is?**

**Explain your answer in detail ,and also explain that how it is different from the 'total number of relation from A to B'.**

Suppose A contain m elements and B contains n elements

So each element of A should have a image in B , means there should not be a empty element in A , otherwise the function is not defined .

So corresponding to each A , it can have n images .

Hence for m elements in A , we have n x n x n .........m times = n

^{m }mappings.

In relations there is no conditions like functions .

So if A has m element and B has n elements , then number of ordered pair is mn

And total number of relation = 2

^{mn}

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