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: 33

Answer

This is the same as the condition that a is the aunt or uncle of c (by blood, not marriage).

Work Step by Step

To find So R we want to find the set of pairs (a, c) such that for some person b, a is a parent of b, and b is a sibling of c. Since brothers and sisters have the same parents, this means that a is also the parent of c. Thus S o R is contained in the relation R. More specifically, (a, c) E S o R if and only if a is the parent of c, and c has a sibling (who is necessarily also a child of a). To find Ro S we want to find the set of pairs (a, c) such that for some person b, a is a sibling of b, and b is a parent of c. This is the same as the condition that a is the aunt or uncle of c (by blood, not marriage).
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