If n(U) = 84 and n(A) = 2n(Aᶜ), where U is the universal set, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 28
A and Aᶜ are disjoint and together contain every element of U, so n(A) + n(Aᶜ) = n(U) = 84. Let n(Aᶜ) = x. The given relation gives n(A) = 2x. Hence 2x + x = 84, so 3x = 84 and x = 28. Therefore, n(Aᶜ) is 28. The finite-set complement formula is essential here.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
A and Aᶜ are disjoint and together contain every element of U, so n(A) + n(Aᶜ) = n(U) = 84. Let n(Aᶜ) = x. The given relation gives n(A) = 2x. Hence 2x + x = 84, so 3x = 84 and x = 28. Therefore, n(Aᶜ) is 28. The finite-set complement formula is essential here.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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