Basic sets

I'm having problems with questions g) and k).

For g), apparantly the answer is i) but it seems to me they're all the same.If |b'| is a finite subset of an infinite set, then |b| must be an infinite set as N is infinite. Is there any difference between saying "b is infinite" and "|b| = infinity"?

For k), apparantly the answer is i) as well, but I still don't understand the notation. Could someone explain it through?.

Page in question: http://i38.tinypic.com/142ev41.jpg

I worked out why i) in g) is different now.

ii) and iii) describe "The set of all subsets of the N that are infinite". This set could include the set of odd or even numbers, for example.

i) on the other hand describes "The set of all subsets of N that are infinite, but have a finite complement". This would disallow the set of even numbers from being in the set, as the complement (the set of odd numbers) is infinite.