If \(U=\mathbb{R}\) and \(A=\{x:-2<x\le6\}\), what is \(A'\)?
Answer and explanation
Correct answer: \((- ,-2]\cup(6, )\)
The interval \(A=(-2,6]\) contains every real number greater than \(-2\) and less than or equal to 6. Its complement in \(\mathbb{R}\) therefore contains the numbers not satisfying that condition: all numbers \(x\le-2\), together with all numbers \(x>6\). Hence \(A'=(-\infty,-2]\cup(6,\infty)\). The endpoint rules reverse in the complement.
Frequently asked questions
What is the correct answer to this question?
\((- ,-2]\cup(6, )\)
Why is this the correct answer?
The interval \(A=(-2,6]\) contains every real number greater than \(-2\) and less than or equal to 6. Its complement in \(\mathbb{R}\) therefore contains the numbers not satisfying that condition: all numbers \(x\le-2\), together with all numbers \(x>6\). Hence \(A'=(-\infty,-2]\cup(6,\infty)\). The endpoint rules reverse in the complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
