Assertion: If \(A\subset B\), then \(\mathcal{P}(A)\subset \mathcal{P}(B)\). Reason: Every subset of \(A\) is also a subset of \(B\), and \(B\) itself is in \(\mathcal{P}(B)\) but not in \(\mathcal{P}(A)\). Choose the correct option.
Answer and explanation
Correct answer: Both assertion and reason are true, and the reason explains it
The assertion is true because every subset of \(A\) is automatically a subset of \(B\) when \(A\subset B\). Hence every element of \(\mathcal{P}(A)\) belongs to \(\mathcal{P}(B)\). The inclusion is proper, not merely equal, because \(B\subseteq B\), so \(B\in\mathcal{P}(B)\); however, \(B\notin\mathcal{P}(A)\), since \(B\) is not a subset of the smaller set \(A\). Thus both the assertion and reason are correct, and the reason explains the assertion.
Frequently asked questions
What is the correct answer to this question?
Both assertion and reason are true, and the reason explains it
Why is this the correct answer?
The assertion is true because every subset of \(A\) is automatically a subset of \(B\) when \(A\subset B\). Hence every element of \(\mathcal{P}(A)\) belongs to \(\mathcal{P}(B)\). The inclusion is proper, not merely equal, because \(B\subseteq B\), so \(B\in\mathcal{P}(B)\); however, \(B\notin\mathcal{P}(A)\), since \(B\) is not a subset of the smaller set \(A\). Thus both the assertion and reason are correct, and the reason explains the assertion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
