If the universal set is U = [-2, 6] and A = (1, 4], what is the complement Aᶜ of A with respect to U?
Answer and explanation
Correct answer: [-2, 1] ∪ (4, 6]
The complement consists of the points in U that do not belong to A. In A = (1, 4], the endpoint 1 is excluded, so 1 belongs to the complement. The endpoint 4 is included, so it does not belong to the complement; the interval resumes immediately after 4. Therefore, relative to U = [-2, 6], Aᶜ = [-2, 1] ∪ (4, 6].
Frequently asked questions
What is the correct answer to this question?
[-2, 1] ∪ (4, 6]
Why is this the correct answer?
The complement consists of the points in U that do not belong to A. In A = (1, 4], the endpoint 1 is excluded, so 1 belongs to the complement. The endpoint 4 is included, so it does not belong to the complement; the interval resumes immediately after 4. Therefore, relative to U = [-2, 6], Aᶜ = [-2, 1] ∪ (4, 6].
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.
