If |P(P(A))| = 256, what is the value of |A|?
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Answer and explanation
Correct answer: 3
Let |A| = n. The first power set P(A) has 2^n elements. Taking the power set again gives |P(P(A))| = 2^(2^n). The given value is 256 = 2^8, so 2^n = 8. Since 8 = 2^3, it follows that n = 3. Therefore |A| = 3, and option B is correct. The nested power set must be handled by applying the power-set formula twice.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Let |A| = n. The first power set P(A) has 2^n elements. Taking the power set again gives |P(P(A))| = 2^(2^n). The given value is 256 = 2^8, so 2^n = 8. Since 8 = 2^3, it follows that n = 3. Therefore |A| = 3, and option B is correct. The nested power set must be handled by applying the power-set formula twice.
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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