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Solved: Relate to inhabitants of the island of knights and

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

Solution for problem 20E Chapter 1.2

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 20E

Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine, if possible, what A and B are if they address you in the ways described. If you cannot determine what these two people arc, can you draw any conclusions?A says “The two of us are both knights” and B says “A is a knave.”

Step-by-Step Solution:

SolutionStep 1In this problem we have to find who A and B are.Given: Knights always tell the truth and Knaves always lie.A says “The two of us are both Knights” and B says “A is a knave”Suppose A is a Knight. … (1)Then what A says must be true. (Since knights always tell the truth).Therefore B is also a Knight.But B says “A is a knave”. … (2)From (1) and (2) we get,A is both knight and knave, which is impossible.So what B says is correct.is a knave.Therefore “The two of us are both Knights” is false.is a knight.Hence A is a knave and B is a Knight.

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Chapter 1.2, Problem 20E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Solved: Relate to inhabitants of the island of knights and