Let S be the set of positive integers defined by: Basis step: 4 € S. Recursive step: If n e S, then 5n +2 € S and n? e S. (a) Find four elements of S that are less than 120. (b) What is the remainder of each of the four elements of S you listed above when they are each divided by 6. Note: You should get the same number. Show the math for each number. (c) State a hypothesis about the remainder of any element of S when the element is divided by 6. Explain how you would use structural induction over the set S to prove your hypothesis. Note: You do not need to actually prove your hypothesis, but clearly explain the steps you would take including the basis step and the inductive sten

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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Let S be the set of positive integers defined by:
Basis step: 4 € S.
Recursive step: If nE S, then 5n +2 e S and n? e S.
(a) Find four elements of S that are less than 120.
(b) What is the remainder of each of the four elements of S you listed above when they are each divided
by 6. Note: You should get the same number. Show the math for each number.
(c) State a hypothesis about the remainder of any element of S when the element is divided by 6. Explain
how you would use structural induction over the set S to prove your hypothesis. Note: You do not need
to actually prove your hypothesis, but clearly explain the steps you would take including the basis step
and the inductive step.
Transcribed Image Text:Let S be the set of positive integers defined by: Basis step: 4 € S. Recursive step: If nE S, then 5n +2 e S and n? e S. (a) Find four elements of S that are less than 120. (b) What is the remainder of each of the four elements of S you listed above when they are each divided by 6. Note: You should get the same number. Show the math for each number. (c) State a hypothesis about the remainder of any element of S when the element is divided by 6. Explain how you would use structural induction over the set S to prove your hypothesis. Note: You do not need to actually prove your hypothesis, but clearly explain the steps you would take including the basis step and the inductive step.
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