If \(A=\{x\in\mathbb{Z}\mid -4\le x\le4\}\) and \(B=\{x\in\mathbb{Z}\mid x^2\ge9\}\), what is \(A\cap B\)?
Answer and explanation
Correct answer: \(\{-4,-3,3,4\}\)
The set \(A\) contains every integer from \(-4\) through 4. The condition \(x^2\ge9\) is equivalent to \(|x|\ge3\), so among the integers in that interval the valid values are \(-4,-3,3,4\). Values such as \(-2,-1,0,1,2\) have squares less than 9. Therefore, \(A\cap B=\{-4,-3,3,4\}\), which is option A.
Frequently asked questions
What is the correct answer to this question?
\(\{-4,-3,3,4\}\)
Why is this the correct answer?
The set \(A\) contains every integer from \(-4\) through 4. The condition \(x^2\ge9\) is equivalent to \(|x|\ge3\), so among the integers in that interval the valid values are \(-4,-3,3,4\). Values such as \(-2,-1,0,1,2\) have squares less than 9. Therefore, \(A\cap B=\{-4,-3,3,4\}\), which is option A.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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