If only A = 14, only B = 18, only C = 16, only A ∩ B = 7, only B ∩ C = 6, only C ∩ A = 5, and A ∩ B ∩ C = 4, what is n(A ∪ B ∪ C)?
Answer and explanation
Correct answer: 70
The union A ∪ B ∪ C consists of every region lying inside at least one of the three sets. Since the question gives the seven mutually exclusive interior regions, we add them once each: 14 + 18 + 16 + 7 + 6 + 5 + 4 = 70. The triple-intersection value is already one separate region, so it must not be added again through another formula.
Frequently asked questions
What is the correct answer to this question?
70
Why is this the correct answer?
The union A ∪ B ∪ C consists of every region lying inside at least one of the three sets. Since the question gives the seven mutually exclusive interior regions, we add them once each: 14 + 18 + 16 + 7 + 6 + 5 + 4 = 70. The triple-intersection value is already one separate region, so it must not be added again through another formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
