Discrete Mathematics with Applications 4th Edition

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

Chapter 1 - Speaking Mathematically - Exercise Set 1.2 - Page 13: 7


a. $S=\{-1,1\}$ b. $T=\{0,2\}$ c. $U=\{\}$ d. $V=\{...-3,-2,-1,0,1,2,3...\}$ e. $W=\{\}$ f. $X=\{...-3,-2,-1,0,1,2,3...\}$

Work Step by Step

For (a) and (b), the two elements in each set are the result of the arbitrary integer being either even or odd. In (c) and (e), the two sets are empty sets because there are no numbers that are simultaneously greater than a positive number and less than a negative number. In (d) and (f), every integer meets at least one of the two given conditions, so the sets are equal to $Z$, the set of all integers.
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