If A = {x ∈ ℝ : −3 ≤ x < 5}, B = {x ∈ ℝ : 1 < x ≤ 8}, and C = {x ∈ ℝ : x ≤ 2}, what is (A ∪ B) ∩ C?
Answer and explanation
Correct answer: [−3, 2]
A is the interval [−3, 5), while B is (1, 8]. These intervals overlap, so their union covers every real number from −3 through 8, namely A ∪ B = [−3, 8]. Intersecting this union with C = (−∞, 2] keeps only numbers up to and including 2. The left endpoint −3 remains included, giving [−3, 2]. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
[−3, 2]
Why is this the correct answer?
A is the interval [−3, 5), while B is (1, 8]. These intervals overlap, so their union covers every real number from −3 through 8, namely A ∪ B = [−3, 8]. Intersecting this union with C = (−∞, 2] keeps only numbers up to and including 2. The left endpoint −3 remains included, giving [−3, 2]. Therefore, 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).
