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