2. (a) LetA+{w e {0,1) # of 1s in w] [# of0s in w]}, ie A - {w e 10,1)"| w contains at least as many 1's as O's) i. Construct a Turing machine M with input alphabet {0,1) that decides A. (Give both a state diagram for M as well as an implementation-level description of M that clearly shows how your machine decides A.) ii. Confirm, by describing appropriate configurations, that your machine M yields the correct results on the following strings: 0, 10, and 101. (b) Let B = {w e {0,1} (# of 1s in w]