IIl: Structural Induction (20 pt.) Given the following recursive definition: Let S be the subset of Z Z defined as: Basis step: (0, 0) E S Recursive step: if (a, b) E S, then: .(a, b +1) E S . (a 1,b 1) ES (a+2,b+1) ES (15 pt.) Prove that a S 2b for any (a,b) E S using structural induction. Answer the following questions a. b. c. d. e. What is the base case? Complete the basis step of the proof by showing that the base case is true. What is the inductive hypothesis? What do you need to show in the inductive step of the proof? Complete the inductive step of the proof