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'.

Mapping is term used in functions.
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  = nmappings.

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 = 2mn

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