If U = {1,2,3,4,5,6,7,8} and Aᶜ = {1,4,7}, what is n(A)?
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Answer and explanation
Correct answer: 5
The universal set has n(U) = 8 elements, while the complement has n(Aᶜ) = 3 elements. Since A and Aᶜ partition U, n(A) + n(Aᶜ) = n(U). Therefore n(A) = 8 − 3 = 5. Equivalently, A consists of the remaining elements {2,3,5,6,8}, which also confirms that its cardinality is 5. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The universal set has n(U) = 8 elements, while the complement has n(Aᶜ) = 3 elements. Since A and Aᶜ partition U, n(A) + n(Aᶜ) = n(U). Therefore n(A) = 8 − 3 = 5. Equivalently, A consists of the remaining elements {2,3,5,6,8}, which also confirms that its cardinality is 5. Hence option B 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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