If \(U=\{x:x\in\mathbb{N},x\le25\}\) and \(A=\{x:x\in U\text{ and }x\text{ is a square number}\}\), how many elements are in \(A'\)?
Answer and explanation
Correct answer: 20
Assuming the standard school convention \(\mathbb{N}=\{1,2,3,\ldots\}\), the universal set contains 25 elements. The square numbers not exceeding 25 are \(1,4,9,16,25\), so \(n(A)=5\). The complement contains all remaining natural numbers from 1 through 25. Therefore \(n(A')=n(U)-n(A)=25-5=20\), making option A correct. Option B counts the square numbers themselves, not the elements of their complement.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Assuming the standard school convention \(\mathbb{N}=\{1,2,3,\ldots\}\), the universal set contains 25 elements. The square numbers not exceeding 25 are \(1,4,9,16,25\), so \(n(A)=5\). The complement contains all remaining natural numbers from 1 through 25. Therefore \(n(A')=n(U)-n(A)=25-5=20\), making option A correct. Option B counts the square numbers themselves, not the elements of their 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.
