If \(A=\{x\mid x\) is a natural-number solution of \(x^2-4=0\}\) and \(B=\{2\}\), which option is correct?
Answer and explanation
Correct answer: \(A=B\)
Solving \(x^2-4=0\) gives \((x-2)(x+2)=0\), so the integer solutions are \(x=2\) and \(x=-2\). However, the definition of \(A\) asks specifically for a natural-number solution. Under the usual school convention, 2 is natural but −2 is not. Hence \(A=\{2\}\), and since \(B=\{2\}\), the two sets are equal. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
Solving \(x^2-4=0\) gives \((x-2)(x+2)=0\), so the integer solutions are \(x=2\) and \(x=-2\). However, the definition of \(A\) asks specifically for a natural-number solution. Under the usual school convention, 2 is natural but −2 is not. Hence \(A=\{2\}\), and since \(B=\{2\}\), the two sets are equal. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
