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: 54

Answer

The given sets aren't equal for all sets $A$ and $B$.

Work Step by Step

Regions in $A'$ (all the regions not in $A$) are: $III, IV$ Regions in $B$ are: $II, III$ Regions in $A'\cap B$ are: $III$ Regions in $A$ are: $I, II$ Regions in $B'$ (all the regions not in $B$) are: $I, IV$ Regions in $A\cup B'$ are: $I, II, IV$ The elements of $A'\cap B$ and $A\cup B'$ are in different regions; therefore, those two sets aren't equal for all sets $A$ and $B$.
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