If the universal set is \(U=\mathbb{R}\) and \(A=\{x\in\mathbb{R}:x<2\text{ or }x\ge8\}\), what is \(A'\)?
Answer and explanation
Correct answer: \([2,8)\)
Set A contains all real numbers less than 2 together with all real numbers at least 8. Its complement must contain numbers satisfying neither condition: they are not less than 2 and are less than 8. Thus \(2\le x<8\), represented by \([2,8)\). The endpoint 2 is included because it is excluded from A, while 8 is excluded because it belongs to A.
Frequently asked questions
What is the correct answer to this question?
\([2,8)\)
Why is this the correct answer?
Set A contains all real numbers less than 2 together with all real numbers at least 8. Its complement must contain numbers satisfying neither condition: they are not less than 2 and are less than 8. Thus \(2\le x<8\), represented by \([2,8)\). The endpoint 2 is included because it is excluded from A, while 8 is excluded because it belongs to A.
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.
