If \(A\) is the empty set, which statement about \(\mathcal{P}(A)\) is correct?
Answer and explanation
Correct answer: \(\mathcal{P}(A)=\{\varnothing\}\)
The empty set has no elements, so its only possible subset is the empty set itself. Therefore, when \(A=\varnothing\), its power set is \(\mathcal{P}(A)=\{\varnothing\}\). Notice the distinction: \(\varnothing\) is the sole element of the power set, whereas \(\{\varnothing\}\) is a set containing one element. Hence the power set has exactly one element, not zero.
Frequently asked questions
What is the correct answer to this question?
\(\mathcal{P}(A)=\{\varnothing\}\)
Why is this the correct answer?
The empty set has no elements, so its only possible subset is the empty set itself. Therefore, when \(A=\varnothing\), its power set is \(\mathcal{P}(A)=\{\varnothing\}\). Notice the distinction: \(\varnothing\) is the sole element of the power set, whereas \(\{\varnothing\}\) is a set containing one element. Hence the power set has exactly one element, not zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
