If A = (−∞, 3] and B = [1, ∞), what is A ∪ B?
Answer and explanation
Correct answer: ℝ
A contains every real number less than or equal to 3, while B contains every real number greater than or equal to 1. The intervals overlap on [1, 3], so there is no gap between them. Numbers below 1 are covered by A, and numbers above 3 are covered by B. Therefore, together they cover every real number, so A ∪ B = ℝ. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
ℝ
Why is this the correct answer?
A contains every real number less than or equal to 3, while B contains every real number greater than or equal to 1. The intervals overlap on [1, 3], so there is no gap between them. Numbers below 1 are covered by A, and numbers above 3 are covered by B. Therefore, together they cover every real number, so A ∪ B = ℝ. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
