If \(U=\mathbb{R}\) and \(A=[-2,4)\), what is \(A'\)?
Answer and explanation
Correct answer: \((-\infty,-2)\cup[4,\infty)\)
Because the universal set is all real numbers, the complement contains every real number outside the interval \([-2,4)\). The endpoint \(-2\) belongs to \(A\) because the left bracket is closed, so it is excluded from the complement. The endpoint \(4\) does not belong to \(A\) because the right parenthesis is open, so \(4\) belongs to the complement. Therefore, \(A'=(-\infty,-2)\cup[4,\infty)\), option A.
Frequently asked questions
What is the correct answer to this question?
\((-\infty,-2)\cup[4,\infty)\)
Why is this the correct answer?
Because the universal set is all real numbers, the complement contains every real number outside the interval \([-2,4)\). The endpoint \(-2\) belongs to \(A\) because the left bracket is closed, so it is excluded from the complement. The endpoint \(4\) does not belong to \(A\) because the right parenthesis is open, so \(4\) belongs to the complement. Therefore, \(A'=(-\infty,-2)\cup[4,\infty)\), option 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.
