If U = ℝ and A = (2, 5), what is Aᶜ?
Answer and explanation
Correct answer: (−∞, 2] ∪ [5, ∞)
The interval A = (2,5) contains real numbers strictly greater than 2 and strictly less than 5; its endpoints are excluded. Therefore, in the universal set ℝ, the complement contains every real number at most 2 and every real number at least 5. In interval notation this is (−∞,2] ∪ [5,∞). Option A wrongly excludes the endpoints, while option D is A itself.
Frequently asked questions
What is the correct answer to this question?
(−∞, 2] ∪ [5, ∞)
Why is this the correct answer?
The interval A = (2,5) contains real numbers strictly greater than 2 and strictly less than 5; its endpoints are excluded. Therefore, in the universal set ℝ, the complement contains every real number at most 2 and every real number at least 5. In interval notation this is (−∞,2] ∪ [5,∞). Option A wrongly excludes the endpoints, while option D is A itself.
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.
