In a survey, n(U) = 150, n(A) = 70, n(B) = 62, and n((A ∪ B)ᶜ) = 32. What is n(A ∩ B)?
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Answer and explanation
Correct answer: 14
The complement of A ∪ B contains the elements outside the union. Therefore, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 150 − 32 = 118. Now apply n(A ∪ B) = n(A) + n(B) − n(A ∩ B): 118 = 70 + 62 − x. Hence x = 132 − 118 = 14. Therefore, n(A ∩ B) is 14, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The complement of A ∪ B contains the elements outside the union. Therefore, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 150 − 32 = 118. Now apply n(A ∪ B) = n(A) + n(B) − n(A ∩ B): 118 = 70 + 62 − x. Hence x = 132 − 118 = 14. Therefore, n(A ∩ B) is 14, so option B 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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