If the universal set is U = ℝ and A = (-∞, -1] ∪ [6, ∞), what is (A′)′?
Answer and explanation
Correct answer: (-∞, -1] ∪ [6, ∞)
The double-complement law states that (A′)′ = A for every subset A of a universal set U. Here, A consists of all real numbers less than or equal to -1 together with all real numbers greater than or equal to 6. Its complement in ℝ is (-1, 6), because -1 and 6 already belong to A. Taking the complement again restores the original set, so the answer is option A.
Frequently asked questions
What is the correct answer to this question?
(-∞, -1] ∪ [6, ∞)
Why is this the correct answer?
The double-complement law states that (A′)′ = A for every subset A of a universal set U. Here, A consists of all real numbers less than or equal to -1 together with all real numbers greater than or equal to 6. Its complement in ℝ is (-1, 6), because -1 and 6 already belong to A. Taking the complement again restores the original set, so the answer is option A.
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.
