Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.2 - Applications of Propositional Logic - Exercises - Page 23: 31

Answer

There are no solutions to this scenario.

Work Step by Step

Person A says "I am not the spy," B says "I am not the spy," and C says "I am not the spy." If A is the spy, then she is choosing to lie and both B and C are telling the truth. Neither of them can be the knave, so A cannot be the spy. If A is the knave, her statement is true. Therefore, she cannot be the knave. Because someone must be the knave, yet this person's statement evaluates to true under this condition, there are no solutions.
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