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 - Page 95: 106

Answer

The required Venn diagram of the provided set is

Work Step by Step

Now use this Sample of Venn diagram and startplacing movies in the regions. So first start with the innermost region V, which contains all the films which are common to all the provided sets A, Band C. So region V contains one element only “Titanic” Now Region II contains all the films which are common in both set A and set B but not in set C. So this region is empty since there is no such element. Region I contains elements which are in set A only which are not the member of set Band set C. So it contains the movie “Eve”. In a similar way, region III contains elements of set B only which are not in set Aand C. So elements are “Wind” and “Eternity”. Region IV contains common element of Aand C but it should not be an element of set B. Since there is no such movie so it is an empty region. Region VI is contains common elements of B and C but should not be an element of setA. So the movie is “Love”only. Region VII contains all the elements of set C only which are not element of set Band set A. So the movies are “Woolf”, “Gump”, “Rings”, “Chicago”. Finally, Region VIII contains all the element of U which are not member of any of the provided sets A, B and C. So the movie “Poppins” is the only element which is not the element of the provided sets A, Band C. Now the mentioned regions from the Venn diagram.
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