If \(A=\{1,2\}\), which is \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \(\{\emptyset,\{1\},\{2\},\{1,2\}\}\)
The power set \(\mathcal{P}(A)\) is the set of all subsets of A. A two-element set has \(2^2=4\) subsets: the empty set \(\emptyset\), the singleton sets \(\{1\}\) and \(\{2\}\), and the whole set \(\{1,2\}\). Therefore option A lists every subset exactly once. The other options omit at least one subset or confuse elements with subsets.
Frequently asked questions
What is the correct answer to this question?
\(\{\emptyset,\{1\},\{2\},\{1,2\}\}\)
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) is the set of all subsets of A. A two-element set has \(2^2=4\) subsets: the empty set \(\emptyset\), the singleton sets \(\{1\}\) and \(\{2\}\), and the whole set \(\{1,2\}\). Therefore option A lists every subset exactly once. The other options omit at least one subset or confuse elements with subsets.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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