In three sets, only A = 19, only B = 23, only C = 17, only A ∩ B = 8, only B ∩ C = 10, only C ∩ A = 6, and A ∩ B ∩ C = 5. What is n(B ∪ C)?
Answer and explanation
Correct answer: 69
The union B ∪ C contains every Venn-diagram region that lies in B or in C. These regions are only B, only C, only A ∩ B, only B ∩ C, only C ∩ A, and the triple intersection. Therefore, n(B ∪ C) = 23 + 17 + 8 + 10 + 6 + 5 = 69. The only region excluded is the part belonging exclusively to A, which is 19. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
69
Why is this the correct answer?
The union B ∪ C contains every Venn-diagram region that lies in B or in C. These regions are only B, only C, only A ∩ B, only B ∩ C, only C ∩ A, and the triple intersection. Therefore, n(B ∪ C) = 23 + 17 + 8 + 10 + 6 + 5 = 69. The only region excluded is the part belonging exclusively to A, which is 19. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
