If \(\mathcal{P}(A)\subseteq\mathcal{P}(B)\), which conclusion is correct?
Answer and explanation
Correct answer: \(A\subseteq B\)
The set \(A\) is itself an element of its power set \(\mathcal{P}(A)\), because every set is a subset of itself. Given \(\mathcal{P}(A)\subseteq\mathcal{P}(B)\), it follows that \(A\in\mathcal{P}(B)\). Membership in \(\mathcal{P}(B)\) means being a subset of \(B\), so \(A\subseteq B\). The other options do not follow from the given power-set inclusion and can fail for ordinary nested sets.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq B\)
Why is this the correct answer?
The set \(A\) is itself an element of its power set \(\mathcal{P}(A)\), because every set is a subset of itself. Given \(\mathcal{P}(A)\subseteq\mathcal{P}(B)\), it follows that \(A\in\mathcal{P}(B)\). Membership in \(\mathcal{P}(B)\) means being a subset of \(B\), so \(A\subseteq B\). The other options do not follow from the given power-set inclusion and can fail for ordinary nested sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
