If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,4,7\}\), how many elements are in \(\mathcal{P}(A')\)?
Answer and explanation
Correct answer: 16
First find the complement relative to \(U\): \(A'=U\setminus A=\{1,3,5,6\}\). Thus \(A'\) has four elements. A finite set with \(n\) elements has \(2^n\) subsets, so its power set has \(2^4=16\) elements. Therefore \(n(\mathcal{P}(A'))=16\), and option C is correct. The answer is not just the number of elements in \(A'\); it counts all its subsets.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
First find the complement relative to \(U\): \(A'=U\setminus A=\{1,3,5,6\}\). Thus \(A'\) has four elements. A finite set with \(n\) elements has \(2^n\) subsets, so its power set has \(2^4=16\) elements. Therefore \(n(\mathcal{P}(A'))=16\), and option C is correct. The answer is not just the number of elements in \(A'\); it counts all its subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
