2. Give a recursive definition of each of these sets of ordered pairs of positive integers.

(a) S = {(a, b) : a Z +, b Z +, and a + b is odd}

(b) S = {(a, b) : a Z +, b Z +, and a | b

(c) S = {(a, b) : a Z +, b Z +, and 3 |(a + b)}