If n(U) = 96 and n(Aᶜ) = (1/3)n(U), what is the value of n(A)?
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Answer and explanation
Correct answer: 64
The complement has one-third as many elements as the universal set, so n(Aᶜ) = (1/3) × 96 = 32. A set and its complement partition the universal set into two non-overlapping parts. Therefore, n(A) + n(Aᶜ) = n(U), and n(A) = 96 − 32 = 64. Thus, option A is correct; 32 is the size of Aᶜ, not A.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The complement has one-third as many elements as the universal set, so n(Aᶜ) = (1/3) × 96 = 32. A set and its complement partition the universal set into two non-overlapping parts. Therefore, n(A) + n(Aᶜ) = n(U), and n(A) = 96 − 32 = 64. Thus, option A is correct; 32 is the size of Aᶜ, not A.
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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