If n(A) = 6 and n(B) = 4, what is n(P(A)) : n(P(B))?
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Answer and explanation
Correct answer: 4 : 1
For any finite set X, the power set has 2ⁿ(X) elements. Therefore n(P(A)) = 2⁶ = 64 and n(P(B)) = 2⁴ = 16. Their ratio is 64:16, which simplifies by dividing both terms by 16 to 4:1. The ratios 3:2 and 6:4 compare the original sets, not their power sets, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
4 : 1
Why is this the correct answer?
For any finite set X, the power set has 2ⁿ(X) elements. Therefore n(P(A)) = 2⁶ = 64 and n(P(B)) = 2⁴ = 16. Their ratio is 64:16, which simplifies by dividing both terms by 16 to 4:1. The ratios 3:2 and 6:4 compare the original sets, not their power sets, so 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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