If \(U=\{1,2,\ldots,25\}\) and \(A=\{x\in U:x\text{ is a perfect square}\}\), what is \(n(A')\)?
Answer and explanation
Correct answer: 20
The perfect squares in the universal set \(U=\{1,2,\ldots,25\}\) are \(1,4,9,16,25\), because they are \(1^2,2^2,3^2,4^2,5^2\), respectively. Thus \(A\) contains five elements. Since \(U\) contains 25 elements and \(A'\) consists of all elements of \(U\) that are not perfect squares, \(n(A')=n(U)-n(A)=25-5=20\). Therefore option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The perfect squares in the universal set \(U=\{1,2,\ldots,25\}\) are \(1,4,9,16,25\), because they are \(1^2,2^2,3^2,4^2,5^2\), respectively. Thus \(A\) contains five elements. Since \(U\) contains 25 elements and \(A'\) consists of all elements of \(U\) that are not perfect squares, \(n(A')=n(U)-n(A)=25-5=20\). Therefore option A is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
