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 2.1 - Page 37: 5


a. Yes, this is a statement. b. No, this is not a statement. c. Yes, this is a statement. d. No, this is not a statement.

Work Step by Step

A statement is defined as a sentence that is either true or false but not both. Sentences (a) and (c) are both statements because (a) is definitely true and cannot be false ($32^{2}=1024$ but $31^{2}=961$) and (c) is definitely false and cannot be true ($2^{6}=64\ne128$). Sentences (b) and (d) are not statements because their truth values depend on what concrete entity is designated to replace the variables "she" and $x$. For example, "she" = "Martha Washington" makes (b) false, but "Maria Chudnovsky" makes it true; similarly, $x=64$ makes (d) true but $x=13.5$ makes it false.
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