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: 60

Answer

a. $IV, V$ and $VI$ b. $IV, V$ and $VI$ c. $(A\cup B)\cap C=(A\cap C)\cup (B\cap C)$

Work Step by Step

a. $A\cup B$ is represented by all regions in the circle for $A$ as well as all the regions in the circle for $B$: regions $I, II, III, IV, V$ and $VI$. $C$ is represented by all regions within the circle for $C$: regions $IV, V, VI$ and $VII$ $(A\cup B)\cap C$ is represented by regions $IV, V$ and $VI$. b. $A\cap C$ is represented by all regions in the circle for $A$ that are also in the circle for $C$: regions $IV$ and $V$. $B\cap C$ is represented by all regions in the circle for $B$ that are also in the circle for $C$: regions $V$ and $VI$. $(A\cap C)\cup (B\cap C)$ is represented by regions $IV, V$ and $VI$. c. We can conclude that $(A\cup B)\cap C=(A\cap C)\cup (B\cap C)$
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