If \(A=\{x\in\mathbb Z:|x|\le 4\}\) and \(B=\{x\in\mathbb Z:x^2\le 9\}\), what is \(A\setminus B\)?
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Answer and explanation
Correct answer: \(\{-4,4\}\)
The inequality \(|x|\le4\) gives \(-4\le x\le4\), so \(A=\{-4,-3,-2,-1,0,1,2,3,4\}\). The condition \(x^2\le9\) is equivalent to \(|x|\le3\), giving \(B=\{-3,-2,-1,0,1,2,3\}\). Removing all elements of \(B\) from \(A\) leaves only \(-4\) and 4. Therefore \(A\setminus B=\{-4,4\}\).
Frequently asked questions
What is the correct answer to this question?
\(\{-4,4\}\)
Why is this the correct answer?
The inequality \(|x|\le4\) gives \(-4\le x\le4\), so \(A=\{-4,-3,-2,-1,0,1,2,3,4\}\). The condition \(x^2\le9\) is equivalent to \(|x|\le3\), giving \(B=\{-3,-2,-1,0,1,2,3\}\). Removing all elements of \(B\) from \(A\) leaves only \(-4\) and 4. Therefore \(A\setminus B=\{-4,4\}\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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