Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.4 Set Operations and Venn Diagrams with Three Sets - Exercise Set 2.4: 56

Answer

Sets (AUB)' and A'∩B are not equal. As the regions of both the sets are different.

Work Step by Step

Set A' represents all the regions belongs to universal set U that does not belongs to A So, The regions III & IV represents the set A'. a) Set (AUB)' represents all the regions of U which does not belongs to set AUB So, The regions IV represents the set (AUB)'. b) Set A'∩B represents the common regions of set A' and B So, The region III represents the set A'∩B. Based on parts a and b, sets (AUB)' and A'∩B are not equal. As the regions of both the sets are different.
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