Answered: 6. Given the following recursively…

6. Given the following recursively defined set S: Basis: 0 € S and 7 € S Recursive rule: if x € S and y = S, then: • x+yЄS • x-yes Prove that every element in S is divisible by 7.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 6DE

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Question

Prove each of the following statements using induction, strong induction,
or structural induction. For each proof, answer the following questions:
• Complete the basis step of the proof.
• 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.

6. Given the following recursively defined set S:
Basis: 0 € S and 7 € S
Recursive rule: if x € S and y = S, then:
• x+yes
• x-yes
Prove that every element in S is divisible by 7.

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