If n(A ∩ B)=20, n(B ∩ C)=18, n(C ∩ A)=16, and n(A ∩ B ∩ C)=6, how many elements are in exactly two sets?
Answer and explanation
Correct answer: 36
The sum of the three pairwise intersections is 20+18+16=54. However, every element in the triple intersection has been counted in all three pairwise intersections. Since the triple intersection contains 6 elements, it contributes three times, so subtract 3×6. The number in exactly two sets is 54−18=36. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
The sum of the three pairwise intersections is 20+18+16=54. However, every element in the triple intersection has been counted in all three pairwise intersections. Since the triple intersection contains 6 elements, it contributes three times, so subtract 3×6. The number in exactly two sets is 54−18=36. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
