Discrete Mathematics with Applications 4th Edition

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

Chapter 6 - Set Theory - Exercise Set 6.1 - Page 350: 13

Answer

a. True, Z+⊆Q since all positive integers can be stated as x/1, which is a rational number. b. False, R-⊈Q since there are negative real numbers that are not rational, such as -√2 and -π. c. False, Q⊈Z since there are rational numbers that are not integers, such as 5/8. d. False, Z- ⋃ Z+ ≠ Z since 0 ϵ Z but 0∉Z- and 0∉Z+ since 0 is neither positive or negative. e. True, since Z- ⋂ Z+ have no common elements. f. True, since Q ⊆R g. True, since Z⊆Q h. True, since Z+ ⊆R i. False, since Q⊈Z

Work Step by Step

a. True, Z+⊆Q since all positive integers can be stated as x/1, which is a rational number. b. False, R-⊈Q since there are negative real numbers that are not rational, such as -√2 and -π. c. False, Q⊈Z since there are rational numbers that are not integers, such as 5/8. d. False, Z- ⋃ Z+ ≠ Z since 0 ϵ Z but 0∉Z- and 0∉Z+ since 0 is neither positive or negative. e. True, since Z- ⋂ Z+ have no common elements. f. True, since Q ⊆R g. True, since Z⊆Q h. True, since Z+ ⊆R i. False, since Q⊈Z
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