If n(A) = 42, n(A ∪ B) = 69, and n(A ∩ B) = 18, what is n(B)?
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Answer and explanation
Correct answer: 45
Use the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the known values gives 69 = 42 + n(B) − 18. Since 42 − 18 = 24, we have 69 = 24 + n(B), so n(B) = 69 − 24 = 45. Equivalently, n(B) = 69 − 42 + 18 = 45. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
Use the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the known values gives 69 = 42 + n(B) − 18. Since 42 − 18 = 24, we have 69 = 24 + n(B), so n(B) = 69 − 24 = 45. Equivalently, n(B) = 69 − 42 + 18 = 45. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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