If A = {x ∈ ℝ : 0 ≤ x < 3} and B = {x ∈ ℝ : 1 < x ≤ 5}, what is A ∪ B?
Answer and explanation
Correct answer: [0, 5]
A contains every real number from 0, including 0, up to but not including 3. B contains every real number greater than 1 through 5, including 5. The intervals overlap on (1, 3), so there is no gap between them. Their union therefore begins at 0 and ends at 5, with both endpoints included. Hence A ∪ B = [0, 5].
Frequently asked questions
What is the correct answer to this question?
[0, 5]
Why is this the correct answer?
A contains every real number from 0, including 0, up to but not including 3. B contains every real number greater than 1 through 5, including 5. The intervals overlap on (1, 3), so there is no gap between them. Their union therefore begins at 0 and ends at 5, with both endpoints included. Hence A ∪ B = [0, 5].
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
