If A ∪ Aᶜ = U, n(A) = 27, and n(Aᶜ) = 33, what is n(U)?
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Answer and explanation
Correct answer: 60
A set and its complement are disjoint, and their union is the universal set. Hence the elements of A and Aᶜ can be counted separately and added: n(U) = n(A ∪ Aᶜ) = n(A) + n(Aᶜ) = 27 + 33 = 60. The subtraction 33 − 27 = 6 is irrelevant here, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
A set and its complement are disjoint, and their union is the universal set. Hence the elements of A and Aᶜ can be counted separately and added: n(U) = n(A ∪ Aᶜ) = n(A) + n(Aᶜ) = 27 + 33 = 60. The subtraction 33 − 27 = 6 is irrelevant here, so option A is correct.
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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