If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{1,4,9\}\), which description correctly identifies \(A'\)?
Answer and explanation
Correct answer: The non-perfect-square numbers in \(U\)
The complement of \(A\) is formed by taking all elements of the universal set that are not in \(A\). Here \(A\) contains the perfect squares \(1,4,9\) from \(U\). Therefore, \(A'=U\setminus A=\{2,3,5,6,7,8\}\), which is precisely the set of non-perfect-square numbers in \(U\). Hence option B is correct; option A describes \(A\), not its complement.
Frequently asked questions
What is the correct answer to this question?
The non-perfect-square numbers in \(U\)
Why is this the correct answer?
The complement of \(A\) is formed by taking all elements of the universal set that are not in \(A\). Here \(A\) contains the perfect squares \(1,4,9\) from \(U\). Therefore, \(A'=U\setminus A=\{2,3,5,6,7,8\}\), which is precisely the set of non-perfect-square numbers in \(U\). Hence option B is correct; option A describes \(A\), not its complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
