If \(A=\{x,y\}\), which of the following must be an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \{x\}
The power set contains subsets of \(A\), not the individual elements of \(A\) written without braces. Since \(x\in A\), the singleton \(\{x\}\) is a subset of \(A\), so \(\{x\}\in\mathcal{P}(A)\). In fact, \(\mathcal{P}(A)=\{\emptyset,\{x\},\{y\},\{x,y\}\}\). Thus option B is the only correctly written member among the listed choices.
Frequently asked questions
What is the correct answer to this question?
\{x\}
Why is this the correct answer?
The power set contains subsets of \(A\), not the individual elements of \(A\) written without braces. Since \(x\in A\), the singleton \(\{x\}\) is a subset of \(A\), so \(\{x\}\in\mathcal{P}(A)\). In fact, \(\mathcal{P}(A)=\{\emptyset,\{x\},\{y\},\{x,y\}\}\). Thus option B is the only correctly written member among the listed choices.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
