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: 19

Answer

(A'∩B) U (A'∩C') = {b}

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} To find (A'∩B) U (A'∩C'), we need to find A' and C'. A' represents all the elements of U which are not in A So, A'={b,c,d,e,f} C' represents all the elements of U which are not in C So, C'={a,g,h} Now, A'∩B={b,c,d,e,f} ∩ {b,g,h} ={b} (List of all common elements in A' and B ) Now, A'∩C'={b,c,d,e,f} ∩ {a,g,h} ={ } (List of all common elements in A' and C' ) (A'∩B) U (A'∩C') = {b} U { } = {b} (List of all elements of (A'∩B) and the elements of (A'∩C') which are not present in (A'∩B))
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