If U = ℝ and A = [−1, 4], what is Aᶜ?
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Answer and explanation
Correct answer: (−∞, −1) ∪ (4, ∞)
The closed interval A = [−1,4] includes both endpoints −1 and 4 as well as every real number between them. Consequently, its complement in ℝ must exclude both endpoints and contain only numbers less than −1 or greater than 4. Therefore Aᶜ = (−∞,−1) ∪ (4,∞), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
(−∞, −1) ∪ (4, ∞)
Why is this the correct answer?
The closed interval A = [−1,4] includes both endpoints −1 and 4 as well as every real number between them. Consequently, its complement in ℝ must exclude both endpoints and contain only numbers less than −1 or greater than 4. Therefore Aᶜ = (−∞,−1) ∪ (4,∞), so 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.
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