If \(A=B\), which relation between \(\mathcal{P}(A)\) and \(\mathcal{P}(B)\) is true?
Answer and explanation
Correct answer: \(\mathcal{P}(A)=\mathcal{P}(B)\)
Equal sets have exactly the same elements and therefore exactly the same subsets. For any set X, \(X\in\mathcal{P}(A)\) means \(X\subseteq A\). Since A and B are equal, this is equivalent to \(X\subseteq B\), which means \(X\in\mathcal{P}(B)\). Thus the two power sets have identical elements and are equal. They are not generally empty.
Frequently asked questions
What is the correct answer to this question?
\(\mathcal{P}(A)=\mathcal{P}(B)\)
Why is this the correct answer?
Equal sets have exactly the same elements and therefore exactly the same subsets. For any set X, \(X\in\mathcal{P}(A)\) means \(X\subseteq A\). Since A and B are equal, this is equivalent to \(X\subseteq B\), which means \(X\in\mathcal{P}(B)\). Thus the two power sets have identical elements and are equal. They are not generally empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
