Question

in the given venn diagram if n(u)=100 , n(a)=60, n(b)=48 n(a intersect b)=22 and n(a intersect c)=30 find the number of elements in each region and find value of n(aub) and n(b' intersect c')

Answer 1

In the given venn diagram if n(U ) = 100 , n(A ) = 60, n(B ) = 48 n(A ∩ B ) = 22 and n(A ∩ C ) = 30

TO DETERMINE

1. The number of elements in each region

2. The value of : n(A ∪ B) and n(B' ∩ C')

EVALUATION

Here it is given that in the given venn diagram

n(U ) = 100 , n(A ) = 60, n(B ) = 48 , n(A ∩ B ) = 22 and n(A ∩ C ) = 30

ANSWER TO QUESTION : 1

The number of elements in each region is referred to the venn diagram

Venn diagram : Venn diagram is referred to the attachment

ANSWER TO QUESTION : 2

Now

n(A ∪ B)

= n(A) + n(B) - n(A ∩ B )

= 60 + 48 - 22

= 86

Again

n(B' ∩ C')

= n((B ∪ C)')'

= n(U) - n(B ∪ C)

= n(U) - [ n(B) + n(C) - n(B ∩ C) ]

= n(U) - n(B) - n(C) + n(B ∩ C)

= 100 - 48 - 30 + 0

= 22

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