If n(U)=60, n(A)= 35, n(B)=24, and n(AUB)'=10 then n(A∩B) is ____________?
Correct answer: C. 9
- A. 10
- B. 8
- C. 9
- D. None of TheseInteractive math quizzes
Explanation
Since n((AUB)') = 10 and n(U) = 60, n(AUB) = 60 - 10 = 50. Using n(AUB) = n(A) + n(B) - n(A∩B), we get 50 = 35 + 24 - n(A∩B), so n(A∩B) = 9. The likely mistake is choosing 10 by confusing the complement of the union with the intersection.
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