Rosen, Discrete Mathematics ,counting

Question

How many partial functions are there from a set with m elements to a set with n
elements, where m and n are positive integers?

Comments

According to me the answer should be $n^{^{m}}$ but according to the book it is $(n+1)^{^{m}}$...

Answer 1

Look Difference between partial function and Total function is that if total function every element of set A has image in Set B but in partial there may be element who done not have image in B, 

So one possibility increases which is no function at all. i.e. (n+1)^m

Comments

but we have maximum n elements in set B and if an element of set A is not related to set B the answer should be $n^{^{(m-1)}}$ ...just saying :) ...

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nah, you create one more choice to every element to take it or not . with phi also .