In three sets, only A = 27, only A ∩ B = 10, only C ∩ A = 12, and A ∩ B ∩ C = 8. What is n(A)?
Answer and explanation
Correct answer: 57
To find n(A), add every disjoint Venn-diagram region that lies inside A. These regions are: only A, only A ∩ B, only A ∩ C, and the common region A ∩ B ∩ C. Therefore, n(A) = 27 + 10 + 12 + 8 = 57. The word “only” means the pairwise regions exclude the triple intersection, so the triple region must be added separately. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
To find n(A), add every disjoint Venn-diagram region that lies inside A. These regions are: only A, only A ∩ B, only A ∩ C, and the common region A ∩ B ∩ C. Therefore, n(A) = 27 + 10 + 12 + 8 = 57. The word “only” means the pairwise regions exclude the triple intersection, so the triple region must be added separately. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
