Let S be the subset of the set of ordered pairs of integers defined recursively by: Base case: (0, 0) ∈ S
Recursive step: If (a, b) ∈ S, then (a + 1, b + 3) ∈ S and (a + 3, 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 5 | a + b when (a, b) ∈ S.
C) Use structural induction to show that 5 | a + b when (a, b) ∈ S.