Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 9 - Section 9.1 - Relations and Their Properties - Exercises - Page 582: 27

Answer

a) $R^(-1) $= {(b,a) | a divide b} or {(a,b)| b divide a} b) $\bar{R}$ = {(a,b) | a doesn't divide b}

Work Step by Step

For the first part, it is asking for the inverse relation. So, since R is a relation from A to B, then the inverse relation is the relation from B to A. It can be denoted as the inverse relation of R : {(b,a) | (a,b) $\in$ R} . For the second part, it is asking for the complementary relation, which is the set of all the ordered pair not in R, which is all pairs that a doesn't divide b.
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