Discrete Mathematics with Applications 4th Edition

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

Chapter 6 - Set Theory - Exercise Set 6.3 - Page 372: 20

Answer

The statement is true. If A and B are any two sets and suppose x ∈ P(A ∩ B). This means that x belongs to both A and B. So, this can also be written as x ∈ P(A ∩ B) = x ∈ P(A) and x ∈ P(B) = x ∈ P (A) ∩ x ∈ P (B) = x ∈ (P (A) ∩ P (B)) = P (A) ∩ P (B)

Work Step by Step

Steps: 1. Break down the function x ∈ P(A ∩ B) by the set intersection rule. 2. The statement is true if you can get P (A) ∩ P (B) by using set intersection rule.
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