Where exactly are you stuck?
Let . Using these sets as domain and co-domain, define functions having the following properties and explain why the properties hold:
a) A function that is not injective and not surjective.
b) A function that is not injective but is surjective.
c) A function that is not surjective but is injective.
d) A function that is bijective.
Well, I'll give you an example for question c): you want it to be injective, but not surjective, that is, you want to distinct elements to have distinct images, but not all elements in the codomain are images from elements of the domain. So, define for instance
satisfies the required conditions. Try working out the other questions: it's really just a matter of knowing the definitions of injective and surjectiveness.