Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • 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
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 37E
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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.
Transcribed Image Text: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.
Given the following recursively defined set S:
Basis: 0 € S and 7 E S
Recursive rule: if x = S and y = S, then:
• x+y=S
• x-yes
Prove that every element in S is divisible by 7.
Transcribed Image Text:Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • x-yes Prove that every element in S is divisible by 7.
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