Structural Induction 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, b1) ES .(a1,b +1) ES .(a 2,b 1) ES al Prove that a 32b 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