If |P(P(A))| = 256, what is |A|?
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Answer and explanation
Correct answer: 3
Let |A| = n. A set with n elements has a power set of size 2ⁿ. Therefore, |P(P(A))| = 2^(2ⁿ). Since 256 = 2⁸, we have 2^(2ⁿ) = 2⁸, which gives 2ⁿ = 8. Because 8 = 2³, n = 3. It is important not to confuse 2^(2ⁿ) with 2^(2n); the exponent is itself 2ⁿ. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Let |A| = n. A set with n elements has a power set of size 2ⁿ. Therefore, |P(P(A))| = 2^(2ⁿ). Since 256 = 2⁸, we have 2^(2ⁿ) = 2⁸, which gives 2ⁿ = 8. Because 8 = 2³, n = 3. It is important not to confuse 2^(2ⁿ) with 2^(2n); the exponent is itself 2ⁿ. Thus option B 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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