Countable Sets For each set defined below, prove that the set described is countable. 1. Evens = {2n | n E N} 2. N U {T, } (where is the ratio of a circle's circumference to its diameter and is the ratio of a circle's circumference to its radius) 3. The set X of all finite state machines, M = (S, G, go) where S = Nk for some natural number k > 0, and G-S S and go E S are otherwise unrestricted. (Note that here we are not working with a fixed k, and for example machines with S = N2 and machines with S = N9 are both counted in the set X)