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What is wrong with this "proof" that all horses are the

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

Solution for problem 49E Chapter 5.1

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 49E

What is wrong with this "proof" that all horses are the same color?

Let P(n) be the proposition that all the horses in a set of n horses are the same color.

Basis Step: Clearly, P(l) is true.

Inductive Step: Assume that P(k) is true, so that all the horses in any set of k horses are the same color. Consider any k + 1 horses; number these as horses 1,2,3,…,k,k + 1. Now the first k of these horses all must have the same color, and the last k of these must also have the same color. Because the set of the first k horses and the set of the last k horses overlap, all k + 1 must be the same color. This shows that P(k + 1) is true and finishes the proof by induction.

Step-by-Step Solution:
Step 1 of 3

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Step 2 of 3

Chapter 5.1, Problem 49E is Solved
Step 3 of 3

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

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