## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 2 - Set Theory - 2.3 Venn Diagrams and Set Operations - Exercise Set 2.3 - Page 81: 53

#### Answer

A'∪C' = {a,b,c,d,e,f,g,h}

#### Work Step by Step

U = {a,b,c,d,e,f,g,h} A = {a,g,h} B = {b,g,h} C = {b,c,d,e,f} The set A' contains all the elements that are not in set A. Since A contains a,g,h so these elements will not be there in set A. Therefore the elements of A' are b,c,d,e,f. A' = {b,c,d,e,f} The set C' contains all the elements that are not in set C. Since C contains b,c,d,e,f so these elements will not be there in set C. Therefore the elements of C' are a,g,h. C' = {a,g,h} A'∪C' shows all the elements of set A' and set C' and excluding repeated ones. List the elements from the first set, namely b,c,d,e,f.. Now add to the list the elements in the second set that are not in the first set. This includes element in the second set, namely a,g,h. The elements of A'∪C' are a,b,c,d,e,f,g,h. Therefore A'∪C' = {a,b,c,d,e,f,g,h}

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