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: 8

Answer

(C'∩A) ∪ (C'∩B') = {1,7}

Work Step by Step

U={1,2,3,4,5,6,7} A={1,3,5,7} B={1,2,3} C={2,3,4,5,6} TO FIND (C'∩A) ∪ (C'∩B') Let's first find B' & C' B'= {4,5,6,7} (All the elements of universal set U which are not there in B) C' = {1,7} (All the elements of universal set U which are not there in C) C'∩A = (1,7} ∩ {1,3,5,7} = {1,7} (Common elements of C' and A) C'∩B' = (1,7} ∩ {4,5,6,7} = {7} (Common elements of C' and B') (C'∩A) ∪ (C'∩B') = {1,7} ∪ {7} = {1,7} (All the elements of (C'∩A) and the elements of (C'∩B') which are not there in (C'∩A))
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