Is (I hate this notation), and in what sense do you mean isomorphism?
If I am right on the notation, I suppose it must be that . Suppose is injective. Let be any function.
We need to find a function so that .
To do this, first note that since is injective, it is actually a bijection ,
so there exists such that for all .
Then define if and otherwise. Then . Since we have found a preimage for an arbitrary element, the function is onto.
See if you can do (b) on your own now.