If n(A) = 92, n(B) = 85, n(C) = 78, n(A ∩ B) = 37, n(B ∩ C) = 34, n(C ∩ A) = 29, and n(A ∩ B ∩ C) = 16, how many elements are only in B ∩ C?
Advertisement
Answer and explanation
Correct answer: 18
The quantity n(B ∩ C) = 34 includes every element common to B and C, including those that also belong to A. The central three-set intersection contains 16 elements. Therefore, the region belonging only to B and C is n(B ∩ C) − n(A ∩ B ∩ C) = 34 − 16 = 18. Thus the correct answer is 18.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The quantity n(B ∩ C) = 34 includes every element common to B and C, including those that also belong to A. The central three-set intersection contains 16 elements. Therefore, the region belonging only to B and C is n(B ∩ C) − n(A ∩ B ∩ C) = 34 − 16 = 18. Thus the correct answer is 18.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement