If n(A ∪ B) = 139, n(A) = 82, n(B) = 76, and n(U) = 190, what is n(Aᶜ ∪ Bᶜ)?
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Answer and explanation
Correct answer: 171
By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. First find the intersection using n(A ∪ B) = n(A) + n(B) − n(A ∩ B): 139 = 82 + 76 − n(A ∩ B), so n(A ∩ B) = 19. The complement of this intersection in the universal set therefore has 190 − 19 = 171 elements. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
171
Why is this the correct answer?
By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. First find the intersection using n(A ∪ B) = n(A) + n(B) − n(A ∩ B): 139 = 82 + 76 − n(A ∩ B), so n(A ∩ B) = 19. The complement of this intersection in the universal set therefore has 190 − 19 = 171 elements. Hence option D 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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