If U = ℝ and A = {x : −3 ≤ x < 4 or 7 < x ≤ 10}, what is A′?
Answer and explanation
Correct answer: (−∞, −3) ∪ [4, 7] ∪ (10, ∞)
The first interval includes −3 but excludes 4, while the second includes 10 but excludes 7. Therefore, points not in A are all real numbers less than −3, the interval from 4 through 7 including both endpoints, and numbers greater than 10. Thus A′ = (−∞, −3) ∪ [4, 7] ∪ (10, ∞), which is option A.
Frequently asked questions
What is the correct answer to this question?
(−∞, −3) ∪ [4, 7] ∪ (10, ∞)
Why is this the correct answer?
The first interval includes −3 but excludes 4, while the second includes 10 but excludes 7. Therefore, points not in A are all real numbers less than −3, the interval from 4 through 7 including both endpoints, and numbers greater than 10. Thus A′ = (−∞, −3) ∪ [4, 7] ∪ (10, ∞), which 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.
