If n(P(A)) = n(P(B)), which conclusion is definitely true?
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Answer and explanation
Correct answer: n(A) = n(B)
For finite sets, n(P(A)) = 2ⁿ(A) and n(P(B)) = 2ⁿ(B). If these two powers are equal, their nonnegative integer exponents must be equal, so n(A) = n(B). This does not imply A = B, because different sets can have the same number of elements; for example, {1,2} and {3,4}.
Frequently asked questions
What is the correct answer to this question?
n(A) = n(B)
Why is this the correct answer?
For finite sets, n(P(A)) = 2ⁿ(A) and n(P(B)) = 2ⁿ(B). If these two powers are equal, their nonnegative integer exponents must be equal, so n(A) = n(B). This does not imply A = B, because different sets can have the same number of elements; for example, {1,2} and {3,4}.
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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