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: 20

Answer

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