If P(A) = P(B), which conclusion is correct?
Answer and explanation
Correct answer: A = B
A set is always an element of its own power set, so A ∈ P(A). If P(A) = P(B), then every subset of A is also a subset of B and vice versa. In particular, each element of A, viewed as a singleton subset, belongs to P(B), which implies that it belongs to B; thus A ⊆ B. By the same argument B ⊆ A. Therefore A = B, so option B is the only valid conclusion. Equal power sets cannot arise from different original sets.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A set is always an element of its own power set, so A ∈ P(A). If P(A) = P(B), then every subset of A is also a subset of B and vice versa. In particular, each element of A, viewed as a singleton subset, belongs to P(B), which implies that it belongs to B; thus A ⊆ B. By the same argument B ⊆ A. Therefore A = B, so option B is the only valid conclusion. Equal power sets cannot arise from different original sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
