If \(A=\{x\in\mathbb{R}:x<0\}\) and \(B=\{x\in\mathbb{R}:x^2\le4\}\), what is \(A\cup B\)?
Answer and explanation
Correct answer: \((-\infty,2]\)
Solving \(x^2\le4\) gives \(-2\le x\le2\), so \(B=[-2,2]\). Set A already contains every negative real number, including all numbers less than -2. Set B adds the interval from -2 through 2, including 2. Their union therefore contains every real number less than or equal to 2, namely \((-\infty,2]\).
Frequently asked questions
What is the correct answer to this question?
\((-\infty,2]\)
Why is this the correct answer?
Solving \(x^2\le4\) gives \(-2\le x\le2\), so \(B=[-2,2]\). Set A already contains every negative real number, including all numbers less than -2. Set B adds the interval from -2 through 2, including 2. Their union therefore contains every real number less than or equal to 2, namely \((-\infty,2]\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
