Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.5 Survey Problems - Exercise Set 2.5: 9

Answer

The number of elements belongs to region I = n(A)-n(A∩B) =14 The number of elements belongs to region III = n(B)-n(A∩B) =22 The number of elements belongs to region IV = n(U)-n(A)-n(B)+n(A∩B) =5

Work Step by Step

From the given Venn diagram, the regions II represents the number of elements in set A and Set B. i.e n(A∩B) and it's given that n (A)= 21 , n(B) =29, n(U) =48 The number of elements belongs to region I = n(A)-n(A∩B) = 21-7 =14. The number of elements belongs to region III = n(B)-n(A∩B) = 29-7 =22. The number of elements belongs to region IV = n(U)-n(A)-n(B)+n(A∩B) = 48-21-29+7 =5.
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