If U = ℝ, A = [−5, 1), and B = (3, 8], what is (A ∪ B)′?
Answer and explanation
Correct answer: (−∞, −5) ∪ [1, 3] ∪ (8, ∞)
The union A ∪ B consists of the interval [−5, 1) together with (3, 8]. Its complement in the real numbers contains values less than −5, the complete interval from 1 to 3, and values greater than 8. The endpoint signs are important: −5 and 8 are included in the original union, so they are excluded from the complement; 1 and 3 are excluded from the original union, so they are included in the complement. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
(−∞, −5) ∪ [1, 3] ∪ (8, ∞)
Why is this the correct answer?
The union A ∪ B consists of the interval [−5, 1) together with (3, 8]. Its complement in the real numbers contains values less than −5, the complete interval from 1 to 3, and values greater than 8. The endpoint signs are important: −5 and 8 are included in the original union, so they are excluded from the complement; 1 and 3 are excluded from the original union, so they are included in the complement. Thus 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.
