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
Accepted Solution
A:
Answer:The correct option is B.Step-by-step 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 getn(A∩B∩C')=n(A∩B)-n(A∩B∩C)= 8-3 = 5n(A∩B'∩C)=n(A∩C)-n(A∩B∩C)= 8-3 = 5n(A'∩B∩C)=n(B∩C)-n(A∩B∩C)= 6-3 = 3n(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 = 22The value of n(A∩(B∪C)') is 22. Therefore the correct option is B.