If the finite universal set \(U\) has \(n(U)=24\) and \(n(A)=n(A^c)\), what is the value of \(n(A)\)?
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Answer and explanation
Correct answer: 12
A set and its complement are disjoint, and their union is the universal set. Hence, \(n(A)+n(A^c)=n(U)=24\). Since the problem states that \(n(A)=n(A^c)\), let each cardinality be \(x\). Then \(x+x=24\), so \(2x=24\) and \(x=12\). Therefore, \(n(A)=12\).
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
A set and its complement are disjoint, and their union is the universal set. Hence, \(n(A)+n(A^c)=n(U)=24\). Since the problem states that \(n(A)=n(A^c)\), let each cardinality be \(x\). Then \(x+x=24\), so \(2x=24\) and \(x=12\). Therefore, \(n(A)=12\).
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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