6. Structural Induction (15 points) Let S be a subset of the set of integers defined recursively as follows: Base case: (0,0) E S Recursive case: If (a, b) E S then (a +1,b+2) S. 1) List the elements of S produced by the first 4 applica- tions of the recursive definition: 2) Use structural induction to show for all (a, b) (a + b) = 3k for some k E N. S that a) Complete the base case: b) Inductive Step