If 𝒫(A) = 𝒫(B), which statement is definitely true?
Advertisement
Answer and explanation
Correct answer: A = B
If 𝒫(A) = 𝒫(B), every subset of A is also a subset of B and every subset of B is also a subset of A. In particular, A is an element of 𝒫(A), so equality of the power sets gives A ∈ 𝒫(B), which means A ⊆ B. Similarly, B ∈ 𝒫(B) gives B ⊆ A. Mutual inclusion implies A = B. Thus option C is definitely true.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
If 𝒫(A) = 𝒫(B), every subset of A is also a subset of B and every subset of B is also a subset of A. In particular, A is an element of 𝒫(A), so equality of the power sets gives A ∈ 𝒫(B), which means A ⊆ B. Similarly, B ∈ 𝒫(B) gives B ⊆ A. Mutual inclusion implies A = B. Thus option C is definitely true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement