If the universal set is \(U=\mathbb{R}\) and \(A=\{x\in\mathbb{R}\mid x<3\text{ or }x\ge 8\}\), what is \(A'\)?
Answer and explanation
Correct answer: \([3,8)\)
The set A contains all real numbers less than 3 and all real numbers greater than or equal to 8. Its complement must therefore contain the real numbers that are not less than 3 and are not at least 8. These conditions are \(x\ge3\) and \(x<8\), giving \(A'=[3,8)\). The endpoint 3 is included, while 8 is excluded, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\([3,8)\)
Why is this the correct answer?
The set A contains all real numbers less than 3 and all real numbers greater than or equal to 8. Its complement must therefore contain the real numbers that are not less than 3 and are not at least 8. These conditions are \(x\ge3\) and \(x<8\), giving \(A'=[3,8)\). The endpoint 3 is included, while 8 is excluded, so option A is correct.
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.
