In three sets, n(A ∪ B ∪ C) = 150. If only A = 32, only B = 28, only C = 24, only A ∩ B = 18, only B ∩ C = 16, and only C ∩ A = 14, what is n(A ∩ B ∩ C)?
Answer and explanation
Correct answer: 18
A three-set Venn diagram has seven mutually exclusive regions inside the union: three regions belonging to exactly one set, three regions belonging to exactly two sets, and the central region belonging to all three. The six stated regions total 32 + 28 + 24 + 18 + 16 + 14 = 132. Since the union contains 150 elements, the central triple-intersection is 150 − 132 = 18. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
A three-set Venn diagram has seven mutually exclusive regions inside the union: three regions belonging to exactly one set, three regions belonging to exactly two sets, and the central region belonging to all three. The six stated regions total 32 + 28 + 24 + 18 + 16 + 14 = 132. Since the union contains 150 elements, the central triple-intersection is 150 − 132 = 18. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
