Question

use a Venn diagram and the given information to n(union) = 103, n(A) = 35, n(B) = 42, n(C) = 45, n(A intersection B) = 8, n(A intersection C) = 8, n(B intersection C) = 6, and n(A intersection (B intersection C) = 3. Find n(A intersection (B union C)'). A) 4 B) 22 C) 3 D) 26

Answer 1

The correct option is B.

Explanation:

Given information: n(A) = 35, n(B) = 42, n(C) = 45, n(A∩B) = 8, n(A∩C) = 8, n(B∩C) = 6, and n(A∩B∩C) = 3.

We need to find the value of n(A∩(B∩C)')

Using venn diagram we get

n(A∩B∩C')=n(A∩B)-n(A∩B∩C)= 8-3 = 5

n(A∩B'∩C)=n(A∩C)-n(A∩B∩C)= 8-3 = 5

n(A'∩B∩C)=n(B∩C)-n(A∩B∩C)= 6-3 = 3

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

n(A∩(B∪C)')=35-5-5-3 = 22

The value of n(A∩(B∪C)') is 22. Therefore the correct option is B.