Question

Let A,B,C be the subset of the universal set U, if n(U) = 692, n(B) = 230, n(C) = 370
n(B∩C) = 90 and n(A∩B'∩C') = 10 then n(A' ∩ B' ∩ C') equals?

Answer 1

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Answer 2

n(A' ∩ B' ∩ C') = 172

Given :

• A , B , C be the subset of the universal set U

• n(U) = 692, n(B) = 230, n(C) = 370 , n(B∩C) = 90 and n(A ∩ B' ∩ C') = 10

To find :

n(A' ∩ B' ∩ C')

Solution :

Step 1 of 2 :

Find n(B' ∩ C')

n(B ∪ C)

= n(B) + n(C) - n(B ∩ C)

= 230 + 370 - 90

= 510

∴ n(B' ∩ C')

= n[(B ∪ C)']

= n(U) - n(B ∪ C)

= 692 - 510

= 182

Step 2 of 2 :

Find n(A' ∩ B' ∩ C')

Let P = B' ∩ C'

∴ n(A' ∩ B' ∩ C')

= n(A' ∩ P)

= n(P) - n(A ∩ P)

= n(B' ∩ C') - n(A ∩ B' ∩ C')

= 182 - 10

= 172

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