If U = ℝ and A = (−∞, −2) ∪ [3, 7], what is A′, the complement of A in ℝ?
Answer and explanation
Correct answer: [−2, 3) ∪ (7, ∞)
The complement contains every real number that is not in A. Because (−∞, −2) excludes −2, the point −2 belongs to A′. The interval [3, 7] includes both endpoints 3 and 7, so neither endpoint belongs to the complement. Numbers between −2 and 3, together with numbers greater than 7, are excluded from A and therefore form A′ = [−2, 3) ∪ (7, ∞).
Frequently asked questions
What is the correct answer to this question?
[−2, 3) ∪ (7, ∞)
Why is this the correct answer?
The complement contains every real number that is not in A. Because (−∞, −2) excludes −2, the point −2 belongs to A′. The interval [3, 7] includes both endpoints 3 and 7, so neither endpoint belongs to the complement. Numbers between −2 and 3, together with numbers greater than 7, are excluded from A and therefore form A′ = [−2, 3) ∪ (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.
