Given the following recursively defined set S: Basis: 0 € S and 7 € S Recursive rule: if x ES and y = S, then: • x+yЄS x-yes Prove that every element in S is divisible by 7. . . (3 pt.) Complete the basis step of the proof. (3 pt.) What is the inductive hypothesis? • (3 pt.) What do you need to show in the inductive step of the proof? . (6 pt.) Complete the inductive step of the proof.

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