If the universal set is U = ℝ, A = (-∞,0) ∪ (4,∞), and B = [-2,6], what is A′ ∩ B?
Answer and explanation
Correct answer: [0,4]
Because the universal set is the real numbers, the complement of A contains all real numbers that are not in (-∞,0) or (4,∞). The endpoints 0 and 4 are excluded from A because both defining intervals are open there. Therefore A′ = [0,4]. Since [0,4] is wholly contained in B = [-2,6], their intersection is [0,4].
Frequently asked questions
What is the correct answer to this question?
[0,4]
Why is this the correct answer?
Because the universal set is the real numbers, the complement of A contains all real numbers that are not in (-∞,0) or (4,∞). The endpoints 0 and 4 are excluded from A because both defining intervals are open there. Therefore A′ = [0,4]. Since [0,4] is wholly contained in B = [-2,6], their intersection is [0,4].
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.
