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: 105

Answer

The Venn diagram of the provided set is:
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Work Step by Step

Using the provided table, place the Country or Regions in the provided Venn diagram: Roster form of provided sets are: \[\begin{align} & U=\left\{ \text{United States,Italy,Russia,East Africa,Japan,England,Iran} \right\} \\ & A=\left\{ \text{United States,Italy,Japan,England} \right\} \\ & B=\left\{ \text{United States,Italy,Japan,England} \right\} \\ & C=\left\{ \text{United States,Italy,Russia} \right\} \end{align}\] To construct a Venn diagram start with the innermost region V, which contains all the countries/regions which are common to all the provided sets A, B and C. So region V contains two elements “United States” and “Italy” Now Region II contains all the countries/regions which are common in both set Aand set B but not in set C. So it contaions two elements “Japan” and “England”. Region I contains elements which are in A only. Not in the set B and C. Since all the elements of Aare used up. So region I is empty. In a similar way, region III is empty since it contains elements of set B only. Region IV is also empty since it contains common element of A and C but it should not be an element of B. So it is also empty. Similarly, Region VI is also empty since it contains common elements of B and C but should not be an element of A. Region VII contains all the elements of set C only which are not element of set B and set A. Finally, Region VIII contains all the element of U which are not member of any of the provided sets A, B and C.
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