If \(U=(-4,6]\) and \(A=[0,2]\), what is \(A^c\)?
Answer and explanation
Correct answer: \((-4,0)\cup(2,6]\)
The complement must contain points of U that are not in A. Since A=[0,2] includes both 0 and 2, those endpoints must be excluded from the complement. The left part is therefore (-4,0), while the right part is (2,6]. The endpoint -4 is excluded because it is excluded from U, and 6 is included because U includes 6. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\((-4,0)\cup(2,6]\)
Why is this the correct answer?
The complement must contain points of U that are not in A. Since A=[0,2] includes both 0 and 2, those endpoints must be excluded from the complement. The left part is therefore (-4,0), while the right part is (2,6]. The endpoint -4 is excluded because it is excluded from U, and 6 is included because U includes 6. Hence 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.
