If n(A) = 4 and n(B) = 3, what is the ratio n(P(A)) : n(P(B))?
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Answer and explanation
Correct answer: 2:1
For a finite set X with n elements, the power set P(X) has 2^n elements because each original element may either be included or excluded from a subset. Therefore, n(P(A)) = 2^4 = 16 and n(P(B)) = 2^3 = 8. Their ratio is 16:8, which simplifies by dividing both terms by 8 to 2:1. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
2:1
Why is this the correct answer?
For a finite set X with n elements, the power set P(X) has 2^n elements because each original element may either be included or excluded from a subset. Therefore, n(P(A)) = 2^4 = 16 and n(P(B)) = 2^3 = 8. Their ratio is 16:8, which simplifies by dividing both terms by 8 to 2:1. Thus option A 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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