If \(U=\{1,2,3,4,5,6\}\) and \(A=\{3,4\}\), the power set \(\mathcal{P}(A')\) is formed from the subsets of which set?
Answer and explanation
Correct answer: \(\{1,2,5,6\}\)
The complement is obtained from the stated universal set: \(A'=U\setminus A=\{1,2,3,4,5,6\}\setminus\{3,4\}=\{1,2,5,6\}\). By definition, \(\mathcal{P}(A')\) is the collection of all subsets of this complement. Therefore the set from which those subsets are formed is \(\{1,2,5,6\}\), so option B is correct. The original set and the universal set are not the base set here.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,5,6\}\)
Why is this the correct answer?
The complement is obtained from the stated universal set: \(A'=U\setminus A=\{1,2,3,4,5,6\}\setminus\{3,4\}=\{1,2,5,6\}\). By definition, \(\mathcal{P}(A')\) is the collection of all subsets of this complement. Therefore the set from which those subsets are formed is \(\{1,2,5,6\}\), so option B is correct. The original set and the universal set are not the base set here.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
