(a) Let \(S\) be the set consisting of all the finite subsets of \(\mathbb{N}\). Prove that \(S\) is countable.
(b) Let \(T\) be the set consisting of all the infinite subsets of \(\mathbb{N}\). Prove that \(T\) is uncountable.
(c) Prove that the set of all functions \(f: \mathbb{N} \rightarrow \mathbb{N}\) is uncountable.