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 449: 19

Answer

A× B ={ (2,6),(2,8),(2,10),(4,6),(4,8),(4,10)} R ={ (2,6),(2,8),(2,10),(4,8)} S ={ (2,6),(4,8)} R∪S = R, R∩S = S

Work Step by Step

as - A ={ 2,4} and B ={ 6,8,10} and defining relations R and S from A to B as follows: For all (x, y) ∈ A× B, -x R y ⇔ x|y - x S y ⇔ y−4= x -A× B ={ (2,6),(2,8),(2,10),(4,6),(4,8),(4,10)} -R ={ (2,6),(2,8),(2,10),(4,8)} -S ={ (2,6),(4,8)} -R∪S = R, R∩S = S
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