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,D+ 3) 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 ke Z. Reminder: In other words (a +b) is divisible by 4