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.