Problem 2 Classify whether the following language Pis decidable, recognizable-but-undecidable, or unrecog- 4pts nizable: P = {(M, A) | M is a TM and A is a DFA and L(M) n L(A) = %). In other words, given a TM M and a DFA A as inputs, the problem P is to check that there is no string accepted by both. Prove your answer. For your proof, you can assume that the problem Arm = {(M,w) | M is a TM and accepts w} is undecidable and the problem NArm = {(Mw) | M is a TM and does not accept w} is unrecognizable. Problem 2 Classify whether the following language Pis decidable, recognizable-but-undecidable, or unrecog- 4pts nizable: P = {(M, A) | M is a TM and A is a DFA and L(M) n L(A) = %). In other words, given a TM M and a DFA A as inputs, the problem P is to check that there is no string accepted by both. Prove your answer. For your proof, you can assume that the problem Arm = {(M,w) | M is a TM and accepts w} is undecidable and the problem NArm = {(Mw) | M is a TM and does not accept w} is unrecognizable