If P(A)=P(B), which conclusion is necessary?
Answer and explanation
Correct answer: A=B
If the power sets P(A) and P(B) are equal, then the original sets must also be equal. One direct reason is that every element of A is a singleton or belongs to a subset of A, and the equality of the power sets makes the same subsets available for B. More simply, A itself is an element of P(A), so it is an element of P(B), and similarly B is an element of P(A); the subset relations force A=B. Therefore, option A is necessary. The other statements are not generally implied.
Frequently asked questions
What is the correct answer to this question?
A=B
Why is this the correct answer?
If the power sets P(A) and P(B) are equal, then the original sets must also be equal. One direct reason is that every element of A is a singleton or belongs to a subset of A, and the equality of the power sets makes the same subsets available for B. More simply, A itself is an element of P(A), so it is an element of P(B), and similarly B is an element of P(A); the subset relations force A=B. Therefore, option A is necessary. The other statements are not generally implied.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
