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The exercise relates to inhabitants of an | Ch 1.2 - 26E

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

Solution for problem 26E 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 26E

The exercise relates to inhabitants of an island on which there are three kinds of people: Knights who always tell the truth, knaves who always lie, and spies (called normals by Smullyan [Sm78]) who can either lie or tell the truth. You encounter three people A, B, and C. You know one of these people is a knight, one is a knave and one is a spy. Each of these three people knows the type of person each of other two is. For each of those situations, if possible, determine whether there is a unique solution and determine who the knave, knight and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.

A says “I am the knave.” B says “I am the knave,” and C says “1 am the knave.”

Step-by-Step Solution:

Solution:

 Step 1:

      In this problem we need to determine who the knave , knight and spy are .

           Given : A says that “ I am the knave ” , B says “ I am the knave ” and C says “ I am the knave ”. Also given that  Knight  who always tell  the truth , knaves  who always lie , and spies who can either lie or tell the truth.

          Knave was always telling lies. So , A , B  and C are not a knave .

          A , B and C must be either Knight or spy. Which is impossible.

                        Therefore , solution is not possible.

Step 2 of 2

Chapter 1.2, Problem 26E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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The exercise relates to inhabitants of an | Ch 1.2 - 26E