Structural Induction Let S be the subset of the set of ordered pairs of integers defined recursively by:
Base case: (0,0) E S
Recursive step: If (a, b) є s, then (a + 1, b + 3) E S and (a +3, b+1) є s.
1) List the elements of S produced by the first four applications.
2) Use structural induction to show for all (a, b) E S that (a+b) = 4k for some k e Z.
Reminder: In other words (a +b) is divisible by 4.