Discrete Mathematics with Applications 4th Edition

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

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.2 - Page 168: 13

Answer

Check Work Step by Step Part

Work Step by Step

Given Statement: The negative of any rational number is rational. a) ∀real numbers r, if r is a rational number, then -r is also a rational number. b) The statement is true. Let r be a rational number, then there exist two integer p, q with q ≠0 such that r = $\frac{p}{q}$ . Now -r = $\frac{-p}{q}$ = $\frac{p1}{q}$ As p is an integer , p1 = -p is also an integer. Therefore -r is the ratio between two integers with no zero denominators. Hence -r is also rational
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