Let s be the subset of the set of ordered pairs of integers defined recursively by: basis step: (0, 0) ∈ s. recursive step: if (a, b) ∈ s, then (a, b + 1) ∈ s, (a + 1, b + 1) ∈ s, and (a + 2, b + 1) ∈ s. a) list the elements of s produced by the first four applications of the recursive definition. b) use strong induction on the number of applications of the recursive step of the definition to show that a ≤ 2b whenever (a, b) ∈ s. c) use structural induction to show that a ≤ 2b whenever (a, b) ∈ s.