Computer Science: An Overview: Global Edition (12th Edition)

Published by Pearson Higher Education
ISBN 10: 1292061162
ISBN 13: 978-1-29206-116-0

Chapter 12 - Theory of Computation - Chapter Review Problems - Page 571: 20

Answer

Not valid

Work Step by Step

This pair of statements form a classic paradox known as the "liar paradox." If we assume the first statement is true, then the second statement must also be true, since the first statement claims it to be true. However, if the second statement is true, then the first statement must be false, as it claims the next statement (the second one) to be true. Conversely, if we assume the first statement is false, then it contradicts itself by claiming the next statement to be true. But if the first statement is false, then the second statement can also be false, making the first statement true, which again leads to a contradiction. This paradox illustrates the inherent self-referential contradiction within the statements, making it impossible to determine their truth values simultaneously. Therefore, the pair of statements is inherently invalid due to the logical contradiction they create.
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