If \(A=\{x\in\mathbb{Z}:-3\le x\le 5\}\) and \(B=\{x\in\mathbb{Z}:x^2\le 9\}\), what is \(A\setminus B\)?
Answer and explanation
Correct answer: \(\{4,5\}\)
The condition defining \(A\) gives all integers from \(-3\) through \(5\), so \(A=\{-3,-2,-1,0,1,2,3,4,5\}\). For \(B\), the inequality \(x^2\le9\) is equivalent to \(|x|\le3\), or \(-3\le x\le3\). Therefore, \(B=\{-3,-2,-1,0,1,2,3\}\). The difference \(A\setminus B\) consists only of elements in \(A\) that are not in \(B\). Removing the seven elements of \(B\) from \(A\) leaves \(\{4,5\}\), so option A is correct. Option C is wrong because \(-3\in B\).
Frequently asked questions
What is the correct answer to this question?
\(\{4,5\}\)
Why is this the correct answer?
The condition defining \(A\) gives all integers from \(-3\) through \(5\), so \(A=\{-3,-2,-1,0,1,2,3,4,5\}\). For \(B\), the inequality \(x^2\le9\) is equivalent to \(|x|\le3\), or \(-3\le x\le3\). Therefore, \(B=\{-3,-2,-1,0,1,2,3\}\). The difference \(A\setminus B\) consists only of elements in \(A\) that are not in \(B\). Removing the seven elements of \(B\) from \(A\) leaves \(\{4,5\}\), so option A is correct. Option C is wrong because \(-3\in B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
