Question: Part ll: Structural Induction (20 pt.) (20 pt.) Given the following recursive definition: Let S be the subset of Z x Z defined as: Basis

Part ll: Structural Induction (20 pt.) (20 pt.) Given the following

Part ll: Structural Induction (20 pt.) (20 pt.) Given the following recursive definition: Let S be the subset of Z x Z defined as: Basis step: (0,0) ES Recursive step: if (a, b) E S, then: 1. (a + 2, b + 3) S . (a + 3, b + 2Jes Prove that a + b is divisible by 5 for any (a,b) S using structural induction. Answer the following questions. (4 pt.) Complete the basis step of the proof by showing that the base case is true. (4 pt.) What is the inductive hypothesis? (4 pt.) What do you need to show in the inductive step of the proof? (8 pt.) Complete the inductive step of the proof. a. b. c. d

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