3. Structural Induction (5 points) 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) s, then (a + 1, b + 3) E S and (a +3, b+1) s. (1) (1 point) List the elements of S produced by the first four applications (2) (4 points) Use structural induction to show for all (a, b) E S that (a+b)- of the recursive definition (this should produce 14 new elements). 4k for some k e Z. Reminder: In other words (a +b) is divisible by 4