If \(A=\{x:x\text{ is a positive divisor of }24\}\), what is \(n(\mathcal{P}(A))\)?
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Answer and explanation
Correct answer: 256
The positive divisors of 24 are \(1,2,3,4,6,8,12,24\), so \(n(A)=8\). Alternatively, from \(24=2^3\times3^1\), the divisor-count formula gives \((3+1)(1+1)=8\). A set with 8 elements has \(2^8=256\) subsets. Therefore \(n(\mathcal{P}(A))=256\), and option C is correct.
Frequently asked questions
What is the correct answer to this question?
256
Why is this the correct answer?
The positive divisors of 24 are \(1,2,3,4,6,8,12,24\), so \(n(A)=8\). Alternatively, from \(24=2^3\times3^1\), the divisor-count formula gives \((3+1)(1+1)=8\). A set with 8 elements has \(2^8=256\) subsets. Therefore \(n(\mathcal{P}(A))=256\), and option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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