1. K is the set of all finite subsets in N: A is finite set in N and K = {A in P(N)}. prove that K is a countable set.

2. we say that A is co-finite set in N if A is an Infinite set in N and A' (the complement of A) is a finite set in N. L is the set of all co-finite subsets in N: A is co-finite set in N and L = { A in P(N)}. prove that L is a countable set.

3. M is the set of the all subsets in N which are infinite and their complements (A') are infinite. prove that M is uncountable set. then find the cardinal number of M.

Thanks!!!