If \(A=\{x: x^2=9\}\) and \(B=\{x: x^2-4=0\}\), what is \(A\cup B\)?
Answer and explanation
Correct answer: \(\{-3,-2,2,3\}\)
First solve the equation defining each set. From \(x^2=9\), we obtain \(x=3\) or \(x=-3\), so \(A=\{-3,3\}\). From \(x^2-4=0\), we get \(x^2=4\), hence \(x=2\) or \(x=-2\), so \(B=\{-2,2\}\). The union contains every element that belongs to either set, without repeating any element. Therefore, \(A\cup B=\{-3,-2,2,3\}\), which is option A. Option B lists only A, option C lists only B, and option D omits 2.
Frequently asked questions
What is the correct answer to this question?
\(\{-3,-2,2,3\}\)
Why is this the correct answer?
First solve the equation defining each set. From \(x^2=9\), we obtain \(x=3\) or \(x=-3\), so \(A=\{-3,3\}\). From \(x^2-4=0\), we get \(x^2=4\), hence \(x=2\) or \(x=-2\), so \(B=\{-2,2\}\). The union contains every element that belongs to either set, without repeating any element. Therefore, \(A\cup B=\{-3,-2,2,3\}\), which is option A. Option B lists only A, option C lists only B, and option D omits 2.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
