If \(A=\{3\}\), which of the following is \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \{\emptyset,\{3\}\}
A power set contains all subsets of the original set. For the singleton set \(A=\{3\}\), the only subsets are the empty set \(\emptyset\) and the set \(\{3\}\) itself. Therefore, \(\mathcal{P}(A)=\{\emptyset,\{3\}\}\), which has two elements. The braces are important: 3 is an element of \(A\), whereas \(\{3\}\) is a subset and an element of the power set.
Frequently asked questions
What is the correct answer to this question?
\{\emptyset,\{3\}\}
Why is this the correct answer?
A power set contains all subsets of the original set. For the singleton set \(A=\{3\}\), the only subsets are the empty set \(\emptyset\) and the set \(\{3\}\) itself. Therefore, \(\mathcal{P}(A)=\{\emptyset,\{3\}\}\), which has two elements. The braces are important: 3 is an element of \(A\), whereas \(\{3\}\) is a subset and an element of the power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
