1. (12 points) Consider the following sets representing computational problems (numbering is from the warmup assignment) Po { P,-M) | M is a DFA over {a, b} and abE L(M)) P-{(M, M,> | M and M, are both DFA over {a, b} and L(M) Po = {(M, M' | M and M, are both DFA over {a, b} and L(M) M) | M is a DFA over {a, b} and |L(M)| = 1} L(M')) L(M')} Prove that each of these four problems is decidable. 1. (12 points) Consider the following sets representing computational problems (numbering is from the warmup assignment) Po { P,-M) | M is a DFA over {a, b} and abE L(M)) P-{(M, M,> | M and M, are both DFA over {a, b} and L(M) Po = {(M, M' | M and M, are both DFA over {a, b} and L(M) M) | M is a DFA over {a, b} and |L(M)| = 1} L(M')) L(M')} Prove that each of these four problems is decidable