If P(A) = P(B), which conclusion is always true?
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Answer and explanation
Correct answer: A = B
A set is itself an element of its power set because every set is a subset of itself. If P(A) = P(B), then A belongs to P(B), so A ⊆ B. Similarly, B belongs to P(A), so B ⊆ A. Two sets that are subsets of each other are equal. Therefore A = B is always true, making option A the only valid conclusion.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A set is itself an element of its power set because every set is a subset of itself. If P(A) = P(B), then A belongs to P(B), so A ⊆ B. Similarly, B belongs to P(A), so B ⊆ A. Two sets that are subsets of each other are equal. Therefore A = B is always true, making option A the only valid conclusion.
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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