If n(A ∩ B ∩ C) = 9, only A ∩ B has 14 elements, only B ∩ C has 11 elements, and only C ∩ A has 13 elements, what is n((A ∩ B) ∪ (B ∩ C) ∪ (C ∩ A))?
Answer and explanation
Correct answer: 47
The union of the three pairwise intersections contains every element that belongs to at least two of the sets. The three exclusive pairwise regions contribute 14, 11, and 13 elements. The central region A ∩ B ∩ C belongs to all three pairwise intersections, but it must be counted only once in their union. Therefore, the required number is 14 + 11 + 13 + 9 = 47, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
The union of the three pairwise intersections contains every element that belongs to at least two of the sets. The three exclusive pairwise regions contribute 14, 11, and 13 elements. The central region A ∩ B ∩ C belongs to all three pairwise intersections, but it must be counted only once in their union. Therefore, the required number is 14 + 11 + 13 + 9 = 47, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
