If \(A=\{x:x^2=9,\ x\in\mathbb{Z}\}\) and \(B=\{-3,3\}\), what is true?
Answer and explanation
Correct answer: \(A=B\)
Solving \(x^2=9\) over the integers gives two solutions: \(x=3\) and \(x=-3\). Therefore, \(A=\{-3,3\}\). This is exactly the same collection of elements as \(B=\{-3,3\}\), so \(A=B\). Option B omits the negative solution, option C incorrectly claims a proper subset, and option D ignores the two integer solutions. Always consider both square roots and the stated domain.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
Solving \(x^2=9\) over the integers gives two solutions: \(x=3\) and \(x=-3\). Therefore, \(A=\{-3,3\}\). This is exactly the same collection of elements as \(B=\{-3,3\}\), so \(A=B\). Option B omits the negative solution, option C incorrectly claims a proper subset, and option D ignores the two integer solutions. Always consider both square roots and the stated domain.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
