For a set A, if n(P(P(A))) = 16, what is n(A)?
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Answer and explanation
Correct answer: 2
If n(A) = n, then the power set P(A) has 2^n elements. Applying the power-set rule a second time, P(P(A)) has 2^(2^n) elements. Here 2^(2^n) = 16 = 2^4, so 2^n = 4 = 2^2. Consequently n = 2, and option B is correct. The formula is applied twice, not once.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
If n(A) = n, then the power set P(A) has 2^n elements. Applying the power-set rule a second time, P(P(A)) has 2^(2^n) elements. Here 2^(2^n) = 16 = 2^4, so 2^n = 4 = 2^2. Consequently n = 2, and option B is correct. The formula is applied twice, not once.
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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