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Show that 2n is O(3n) but that 3n is not O(2n). (Note that

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 13E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 13E

Show that 2n is O(3n) but that 3n is not O(2n). (Note that this is a special case of Exercise 60.)

Step-by-Step Solution:

Solution:Step 1In this problem we have to show that but that Function is called if there exist constant c and k such that where Step 2By method of contradiction we will show that, Let us assume that for a pair of witnesses for c and k exist such that we have whenever n > k. Now, when n >0 we can take log on both side of the inequality Or, Since, we know...

Step 2 of 3

Chapter 3.2, Problem 13E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that 2n is O(3n) but that 3n is not O(2n). (Note that

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