If \(A=\{11,22\}\), which of the following is \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \(\{\emptyset,\{11\},\{22\},\{11,22\}\}\)
The power set is the collection of every subset of the original set. For the two-element set \(A=\{11,22\}\), the subsets are the empty set \(\emptyset\), the singleton sets \(\{11\}\) and \(\{22\}\), and the whole set \(\{11,22\}\). Thus \(\mathcal{P}(A)=\{\emptyset,\{11\},\{22\},\{11,22\}\}\), which has \(2^2=4\) elements. Option D incorrectly lists numbers as elements instead of listing the singleton subsets.
Frequently asked questions
What is the correct answer to this question?
\(\{\emptyset,\{11\},\{22\},\{11,22\}\}\)
Why is this the correct answer?
The power set is the collection of every subset of the original set. For the two-element set \(A=\{11,22\}\), the subsets are the empty set \(\emptyset\), the singleton sets \(\{11\}\) and \(\{22\}\), and the whole set \(\{11,22\}\). Thus \(\mathcal{P}(A)=\{\emptyset,\{11\},\{22\},\{11,22\}\}\), which has \(2^2=4\) elements. Option D incorrectly lists numbers as elements instead of listing the singleton subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
