Given n(U) = 95, n(A′) = 47, n(B′) = 52, and n(A ∩ B) = 18, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 73
Use the complement rule first: n(A) = n(U) − n(A′) = 95 − 47 = 48, and n(B) = 95 − n(B′) = 95 − 52 = 43. Then apply inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 48 + 43 − 18 = 73. Thus option A is correct. The other choices result from omitting or mishandling the complement or intersection.
Frequently asked questions
What is the correct answer to this question?
73
Why is this the correct answer?
Use the complement rule first: n(A) = n(U) − n(A′) = 95 − 47 = 48, and n(B) = 95 − n(B′) = 95 − 52 = 43. Then apply inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 48 + 43 − 18 = 73. Thus option A is correct. The other choices result from omitting or mishandling the complement or intersection.
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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