Discrete Mathematics with Applications 4th Edition

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

Chapter 8 - Relations - Exercise Set 8.1 - Page 448: 3

Answer

a ) 1) 3 | (10 - 1) = 3 | 9 >Yes 9 = 3*{3}, 3 $\in$ Z 2) 3 | ( 1 - 10) = 3| -9 >Yes -9 = 3*{-3}, -3 $\in$ Z 3) 3 | (2 - 2) = 3 | 0 >Yes 0 = 3*{0}, 0 $\in$ Z 4) 3 | (8 - 1) = 3| 7 >No 7 ≠ 3*{p} were p $\in$ Z b) {3,6,9,12,15} c) {4,7,10,13,16} d) {5,8,11,14,17} e) nT0 > n = 3k, k $\in$ Z nT1 > n = 3k+1, k $\in$ Z nT2 > n = 3k+2, k $\in$ Z

Work Step by Step

a ) 1) 3 | (10 - 1) = 3 | 9 >Yes 9 = 3*{3}, 3 $\in$ Z 2) 3 | ( 1 - 10) = 3| -9 >Yes -9 = 3*{-3}, -3 $\in$ Z 3) 3 | (2 - 2) = 3 | 0 >Yes 0 = 3*{0}, 0 $\in$ Z 4) 3 | (8 - 1) = 3| 7 >No 7 ≠ 3*{p} were p $\in$ Z b) {3,6,9,12,15} c) {4,7,10,13,16} d) {5,8,11,14,17} e) nT0 > n = 3k, k $\in$ Z nT1 > n = 3k+1, k $\in$ Z nT2 > n = 3k+2, k $\in$ Z
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