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: 10

Answer

The number of elements belongs to region I =16. The number of elements belongs to region III = 20. The number of elements belongs to region IV = 10.

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)= 23 , n(B) =27, n(U) =53. The number of elements belongs to region I = n(A)-n(A∩B) = 23-7 =16. The number of elements belongs to region III = n(B)-n(A∩B) = 27-7 =20. The number of elements belongs to region IV = n(U)-n(A)-n(B)+n(A∩B) = 53-23-27+7 = 10.
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