Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.3 - Page 63: 38

Answer

A : knave B : knight.

Work Step by Step

Method: Reductio Ad Absurdum (Proof by contradiction) Hypothesis: Let us suppose, on the contrary, that A is a knight. Thus, A spoke the truth and hence A and B are both knights(That's what A said). Thus B also spoke the truth (being a knight) which means A is a knave (that;s what B said). So, we have encountered a contradiction due to our faulty hypothesis. Hence, A is not a knight but is a knave which means B is a knight as he spoke truth
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.