28. Let S be the subset of the set of ordered pairs of integers defined recursively by Basis step: (0, 0) E S. Recursive step: If (a, b) € S, then (a +2, b + 3) € S and (a +3, b+2) E S. a) List the elements of S produced by the first five applications of the recursive definition. b) Use strong induction on the number of applications of the recursive step of the definition to show that 51a + b when (a, b) E S. c) Use structural induction to show that 51a + b when (a, b) E S.

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