TS ICET 23 May 2018 Shift 1 Paper

Directions for questions 54 and 55:

Select thecorrect alternative from the given choices.

Question : 55 of 200

Marks: +1, -0

For any set S. let n(S) denote the number of elements in S. For A ⊑ S. let

A^1

denote set S-A. If A. B. C are three sets such that n(A) = 80. n(B) = 46, n(C) = 38. n

(A∩B∩A^1)

= 20 , n

(B∩C∩A^1)

= 9 , n

(C∩A∩B^1)

= 13. If n(A∩B∩C) = 1 then, n (A∪B∪C) =

Solution:

n(A∩B)=n(A∩B∩C')+n(A∩B∩C)

=20+1=21

n(B∩C)=n(B∩C∩A')+n(A∩B∩C)

9+1=10

n(C∩A)=n(C∩A∩B')+n(A∩B∩C)

= 13 + 1 = 14

n(A∪ B ∪ C) = n(A) + n(B) + n(C)-n(A ∩ B) -n(B ∩ C) -n(C ∩ A) + n(A ∩ B ∩ C)

80+ 46 + 38-21- 10-14 + 1

= 120.

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