If \(U=[-3,7]\) and \(A=(-1,4)\), what is \(A^c\)?
Answer and explanation
Correct answer: \([-3,-1]\cup[4,7]\)
The complement is taken inside the universal interval \([-3,7]\). Set A contains every real number strictly between -1 and 4, but it excludes the endpoints -1 and 4. Therefore those endpoints belong to the complement. The portions outside A, while remaining inside U, are \([-3,-1]\) and \([4,7]\), so \(A^c=[-3,-1]\cup[4,7]\).
Frequently asked questions
What is the correct answer to this question?
\([-3,-1]\cup[4,7]\)
Why is this the correct answer?
The complement is taken inside the universal interval \([-3,7]\). Set A contains every real number strictly between -1 and 4, but it excludes the endpoints -1 and 4. Therefore those endpoints belong to the complement. The portions outside A, while remaining inside U, are \([-3,-1]\) and \([4,7]\), so \(A^c=[-3,-1]\cup[4,7]\).
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.
