If only A = 18, only B = 22, only C = 19, only A ∩ B = 9, only B ∩ C = 8, only C ∩ A = 7, and A ∩ B ∩ C = 6, what is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 89
The union of three sets includes every region inside at least one of the three circles. Because the values are given as ‘only’ regions, each region must be added exactly once: 18 + 22 + 19 + 9 + 8 + 7 + 6 = 89. Hence, n(A ∪ B ∪ C) = 89, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
89
Why is this the correct answer?
The union of three sets includes every region inside at least one of the three circles. Because the values are given as ‘only’ regions, each region must be added exactly once: 18 + 22 + 19 + 9 + 8 + 7 + 6 = 89. Hence, n(A ∪ B ∪ C) = 89, so option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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