https://gyazo.com/7a13cab81573c2680c1c9c8d0c636437

Let T_1, T_2, T_3, T_n, be a constructive enumeration of all Turing machines with alphabet {1, 0} and one linear tape. For each of the following sets X_1 = { p: p is a prime number), X_2 = {px: p is a fixed prime number and x is a number of a Turing machine T_x that halts given the input x}, X_3 = {x: x is a number of a Turing machine T_x that does not halt given the input x}, find if it is: a) decidable/recursive: b) recursively enumerable: c) inductively decidable