If \(A=\{x\in\mathbb{R}:x^2<9\}\) and \(B=\{x\in\mathbb{R}:x\ge1\}\), what is \(A-B\)?
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Answer and explanation
Correct answer: \((-3,1)\)
The inequality \(x^2<9\) is equivalent to \(-3<x<3\), so \(A=(-3,3)\). Set B contains 1 and every real number greater than 1. The difference \(A-B\) retains elements of A that are not in B, so all numbers from -3 up to but not including 1 remain. Thus \(A-B=(-3,1)\).
Frequently asked questions
What is the correct answer to this question?
\((-3,1)\)
Why is this the correct answer?
The inequality \(x^2<9\) is equivalent to \(-3<x<3\), so \(A=(-3,3)\). Set B contains 1 and every real number greater than 1. The difference \(A-B\) retains elements of A that are not in B, so all numbers from -3 up to but not including 1 remain. Thus \(A-B=(-3,1)\).
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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