If \(U=\{x\in\mathbb{Z}\mid -3\le x\le 7\}\) and \(A=\{x\in U\mid x+2>4\}\), what is \(A'\), the complement of \(A\) in \(U\)?
Answer and explanation
Correct answer: \(\{-3,-2,-1,0,1,2\}\)
First solve the defining inequality: \(x+2>4\) gives \(x>2\). Since \(x\) must be an integer in \(U=\{-3,-2,-1,0,1,2,3,4,5,6,7\}\), we obtain \(A=\{3,4,5,6,7\}\). The complement consists of the remaining elements of \(U\), namely \(A'=\{-3,-2,-1,0,1,2\}\). Thus option A is correct. The endpoint 2 is included in the complement because the inequality is strict.
Frequently asked questions
What is the correct answer to this question?
\(\{-3,-2,-1,0,1,2\}\)
Why is this the correct answer?
First solve the defining inequality: \(x+2>4\) gives \(x>2\). Since \(x\) must be an integer in \(U=\{-3,-2,-1,0,1,2,3,4,5,6,7\}\), we obtain \(A=\{3,4,5,6,7\}\). The complement consists of the remaining elements of \(U\), namely \(A'=\{-3,-2,-1,0,1,2\}\). Thus option A is correct. The endpoint 2 is included in the complement because the inequality is strict.
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.
