If U = R and A = {x ∈ R : −5 ≤ x < −1 or 2 < x ≤ 7}, what is A'?
Answer and explanation
Correct answer: (-∞, -5) ∪ [-1, 2] ∪ (7, ∞)
The first part of A includes −5 but excludes −1, while the second part excludes 2 but includes 7. Therefore numbers outside A are less than −5, from −1 through 2 including both endpoints, and greater than 7. In interval notation the complement is (−∞, −5) ∪ [−1, 2] ∪ (7, ∞). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
(-∞, -5) ∪ [-1, 2] ∪ (7, ∞)
Why is this the correct answer?
The first part of A includes −5 but excludes −1, while the second part excludes 2 but includes 7. Therefore numbers outside A are less than −5, from −1 through 2 including both endpoints, and greater than 7. In interval notation the complement is (−∞, −5) ∪ [−1, 2] ∪ (7, ∞). 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.
