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Solved: Prove that the recursive algorithm for finding the

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

Solution for problem 40E Chapter 5.4

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 40E

Prove that the recursive algorithm for finding the concatenation of i copies of a bit string that you gave in Exercise 38 is correct.

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MODULE 14: INDUCTION AND RECURSIVE DEFINITION/ALGORITHM Induction/Recursive Definition Algorithm Chapter Summary  Mathematical Induction  Strong Induction  Well-Ordering  Recursive Definitions  Structural Induction  Recursive Algorithms → 5.1 Mathematical Induction ← Climbing an Infinite Ladder Suppose we have an infinite ladder: 1. We can reach the first rung of the ladder. 2. If we can reach a particular rung of the ladder, then we can reach the next rung.  From (1), we can reach the first rung. Then by applying (2), we can reach the second rung. Applying (2) again, the third rung. And so on. We can apply (2) as many times as we feel to reach any particular rung no matter the height. This is proof by mathematical induction. Principle of Mathematical Induction “To prove that P(n) is true for all positive integers n, we complete these steps:  Basis Step: Show that P(1) is true.  Inductive Step: Show that P(k) → P(k + 1) is true for all positive integer k. To complete the inductive step, assuming the INDUCTIVE HYPOTHESIS that P(k) holds for an arbitrary integer k, show that P(k + 1) must be true.” Looking at the “Climbing an Infinite Ladder” example:  BASIS STEP: By (1), WE CAN reach rung 1.  INDUCTIVE STEP: Assume the inductive hypothesis that we can reach rung k. Apply (2) and we can reach rung k + 1. Hence, P(k) → P(k + 1) is true for all positive integers k. We can reach every rung on the ladder. Important Points about MI (Math

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Chapter 5.4, Problem 40E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. This full solution covers the following key subjects: Algorithm, bit, concatenation, copies, correct. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 40E from 5.4 chapter was answered, more than 332 students have viewed the full step-by-step answer. The answer to “Prove that the recursive algorithm for finding the concatenation of i copies of a bit string that you gave in Exercise 38 is correct.” is broken down into a number of easy to follow steps, and 24 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 40E from chapter: 5.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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