If U = ℝ, A = (−6, 1] and B = [−2, 5), what is (A ∪ B)′?
Answer and explanation
Correct answer: (−∞, −6] ∪ [5, ∞)
The two intervals overlap, so their union extends continuously from −6 to 5. The left endpoint −6 is excluded because it is excluded from A, and the right endpoint 5 is excluded because it is excluded from B. Thus A ∪ B = (−6, 5). Taking the complement in ℝ gives (−∞, −6] ∪ [5, ∞), including both boundary points in the complement.
Frequently asked questions
What is the correct answer to this question?
(−∞, −6] ∪ [5, ∞)
Why is this the correct answer?
The two intervals overlap, so their union extends continuously from −6 to 5. The left endpoint −6 is excluded because it is excluded from A, and the right endpoint 5 is excluded because it is excluded from B. Thus A ∪ B = (−6, 5). Taking the complement in ℝ gives (−∞, −6] ∪ [5, ∞), including both boundary points in the complement.
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.
