Need help on the following problem:

Let A={1,2,3,4,5,6}. In each case, give an example of a function f:A->A with the indicated properties, or explain why no such function exists.

a) f is bijective, but not 1A.

b) f is one-to-one, but not onto

Now set A=N (natural numbers)

a) f is bijective, but not 1A.

b) f is one-to-one, but not onto