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Q(n) = { 4 2.Q(n-1)-3 if n = 0 if n>0

Q(n) = { 4 2.Q(n-1)-3 if n = 0 if n>0

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Consider the following recurrence relation:

<<<image here>>>

Prove by induction that Q(n) = 2n + 3, for all n ≥ 0

List the values of Q(n) for n less than or equal 10

 

  1. Describe the difference in proof by contraposition and proof by contradiction. List an example applicable to each.
The given expression is a recursive function definition for \( Q(n) \). It is defined as follows: - \( Q(n) = 4 \) when \( n = 0 \) - \( Q(n) = 2 \cdot Q(n-1) - 3 \) when \( n > 0 \) This function specifies that for the base case when \( n \) is zero, the result is 4. For any positive integer \( n \), the value of the function is determined by doubling the result of the function for \( n-1 \) and then subtracting 3.
Transcribed Image Text:The given expression is a recursive function definition for \( Q(n) \). It is defined as follows: - \( Q(n) = 4 \) when \( n = 0 \) - \( Q(n) = 2 \cdot Q(n-1) - 3 \) when \( n > 0 \) This function specifies that for the base case when \( n \) is zero, the result is 4. For any positive integer \( n \), the value of the function is determined by doubling the result of the function for \( n-1 \) and then subtracting 3.
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Q(n) = 2n + 3, for all n ≥ 0

 

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