If \(\mathcal{P}(A)=\mathcal{P}(B)\), which conclusion is correct?
Answer and explanation
Correct answer: \(A=B\)
Every set is an element of its own power set because a set is always a subset of itself. Thus \(A\in\mathcal{P}(A)\). If \(\mathcal{P}(A)=\mathcal{P}(B)\), then A also belongs to \(\mathcal{P}(B)\), so \(A\subseteq B\). Similarly, B belongs to \(\mathcal{P}(A)\), giving \(B\subseteq A\). By mutual inclusion, \(A=B\).
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
Every set is an element of its own power set because a set is always a subset of itself. Thus \(A\in\mathcal{P}(A)\). If \(\mathcal{P}(A)=\mathcal{P}(B)\), then A also belongs to \(\mathcal{P}(B)\), so \(A\subseteq B\). Similarly, B belongs to \(\mathcal{P}(A)\), giving \(B\subseteq A\). By mutual inclusion, \(A=B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
