If \(\mathcal{P}(A)\) has 16 elements, how many elements does \(A\) have?
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Answer and explanation
Correct answer: 4
If a finite set \(A\) has \(n\) elements, then its power set has \(2^n\) elements. Here, \(|\mathcal{P}(A)|=16\), so \(2^n=16\). Since \(16=2^4\), it follows that \(n=4\). Therefore, the original set \(A\) contains 4 elements. The answer is not 8; 8 would be the number of subsets of a three-element set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
If a finite set \(A\) has \(n\) elements, then its power set has \(2^n\) elements. Here, \(|\mathcal{P}(A)|=16\), so \(2^n=16\). Since \(16=2^4\), it follows that \(n=4\). Therefore, the original set \(A\) contains 4 elements. The answer is not 8; 8 would be the number of subsets of a three-element set.
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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