If \(A=\{\{2\},4,6\}\), what is \(n(\mathcal{P}(A))\)?
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Answer and explanation
Correct answer: 8
The power set of a finite set with \(n\) elements contains \(2^n\) subsets. Here the outer elements of \(A\) are \(\{2\}\), 4, and 6, so \(n(A)=3\). The fact that \(\{2\}\) contains the number 2 does not add another outer element to \(A\). Therefore \(n(\mathcal{P}(A))=2^3=8\), and option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The power set of a finite set with \(n\) elements contains \(2^n\) subsets. Here the outer elements of \(A\) are \(\{2\}\), 4, and 6, so \(n(A)=3\). The fact that \(\{2\}\) contains the number 2 does not add another outer element to \(A\). Therefore \(n(\mathcal{P}(A))=2^3=8\), 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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