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: 7

Answer

The statement is false. Counterexample Let A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8, 10}, and C = {1, 3, 5, 7}. Then A − B = {1, 3, 5}, C − B = {1, 3, 5, 7}, B U C = {1, 2, 3, 4, 5, 6, 7, 8, 10} (A – B) ∩ (C – B) = {1, 3, 5} and A – (B U C) = ∅ Here, we see that (A – B) ∩ (C – B) and A – (B U C) are not equal. Therefore (A – B) ∩ (C – B) ≠ A – (B U C)

Work Step by Step

Steps: 1. Take a counterexample with some arbitrary sets A, B, and C. 2. Compute the value of (A – B) ∩ (C – B) and A – (B U C). 3. Show that these two values are not equal.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.