Discrete Mathematics with Applications 4th Edition

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

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.1: 2

Answer

a. True. The integers correspond to certain of the points on a number line (the numbers that can be written without a fractional component), and the real numbers correspond to all the points on the number line. The integers are a subset of the rational numbers. The rational numbers are a subset of the real numbers. Hence integers are a subset of the real numbers. b. False. 0 is neither positive nor negative. c. False. Let r = -2. The -r = -(-2) = 2 which is positive. d. False. Consider the real number 2.2, which is not an integer.

Work Step by Step

Recall that for all, every, for any, for each, given any are ways to express the quantifier $\forall$ (for all). There exists, for some, for at least one are ways to express the quantifier $\exists$.
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