If U = ℝ and A = {x : 0 < x < 2 or 5 ≤ x < 9}, what is A'?
Answer and explanation
Correct answer: (-∞,0] ∪ [2,5) ∪ [9,∞)
The set A contains the open interval (0,2), so its complement contains x ≤ 0 and x ≥ 2 around that interval. It also contains [5,9), so its complement contains x < 5 and x ≥ 9 in the corresponding region; combining the portions gives [2,5) between the two intervals. Therefore, over ℝ, A' = (-∞,0] ∪ [2,5) ∪ [9,∞). Endpoint symbols are determined by whether the endpoint was included in A.
Frequently asked questions
What is the correct answer to this question?
(-∞,0] ∪ [2,5) ∪ [9,∞)
Why is this the correct answer?
The set A contains the open interval (0,2), so its complement contains x ≤ 0 and x ≥ 2 around that interval. It also contains [5,9), so its complement contains x < 5 and x ≥ 9 in the corresponding region; combining the portions gives [2,5) between the two intervals. Therefore, over ℝ, A' = (-∞,0] ∪ [2,5) ∪ [9,∞). Endpoint symbols are determined by whether the endpoint was included in 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.
