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 8.2 - Page 458: 22

Answer

Not Reflexive Symmetric Not Transitive

Work Step by Step

Let X = {a, b, c} and P(X) be the power set of X. A relation N is defined on P(X) as follows: For all A, B ∈ P(X), A N B ⇔ the number of elements in A is not equal to the number of elements in B. Reflexive: for every A $\in$ P(X) ANA it invalidates the relation since the number of elements in A is the same number of elements in A itself. Symmetric: for every A, B $\in$ P(X) if ANB THEN BNA let ANB be true, which means A doesn't have equal elements as B, which also implies that B doesn't have equal elements as A, then by definition of N BNA ( HENCE TRUE) Transitive: If ANB and BNC then ANC for all A, B, C $\in$ P(X) let A be a set with 8 elements, B with 5, C with 8. which implies that ANB and BNC but ANC is false since A and C have 8 elements each. which implies that the relation is not transitive.
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