(a) Prove that, for any nonempty set A, \\AI 3 l'P(A)|. (Note: A can be an innite set.) (b.) For each of the following statements, indicate if it is true or false and justify your answer. (i.) l'P(Sg)| = \\N\\ where 8'2 is the set of DNA strands of length one or two. (ii.) '8' = ILl where S is the set of DNA strands and L is the set of linked lists. (iii.) \\LS| = lL| where LS is the set of linked lists sorted in nondecreasing order and L is the set of linked lists