3. (a) In class, we used diagonalization to show that the set R of real numbers is uncountably infinite and to construct an example of an undecidable language. Generalize the diago- nalization method used in class to prove that for a countably infinite set A, the power set P(A) is uncountably infinite. Note: The power set of a set A is the set of all subsets of A. For instance, P({0,1}) = {0,{0}, {1},{0,1}}. (b) Prove or disprove: all finite languages are decidable. (c) Prove that any infinite language L has an undecidable subset L' CL. 3. (a) In class, we used diagonalization to show that the set R of real numbers is uncountably infinite and to construct an example of an undecidable language. Generalize the diago- nalization method used in class to prove that for a countably infinite set A, the power set P(A) is uncountably infinite. Note: The power set of a set A is the set of all subsets of A. For instance, P({0,1}) = {0,{0}, {1},{0,1}}. (b) Prove or disprove: all finite languages are decidable. (c) Prove that any infinite language L has an undecidable subset L' CL