If U = ℝ and A = (2, 7], what is A′?
Answer and explanation
Correct answer: (−∞, 2] ∪ (7, ∞)
The complement contains all real numbers that are not in A = (2, 7]. The number 2 is excluded from A because the left endpoint is open, so 2 belongs to A′. The number 7 is included in A because the right endpoint is closed, so 7 does not belong to A′. Thus A′ = (−∞, 2] ∪ (7, ∞), making option A correct.
Frequently asked questions
What is the correct answer to this question?
(−∞, 2] ∪ (7, ∞)
Why is this the correct answer?
The complement contains all real numbers that are not in A = (2, 7]. The number 2 is excluded from A because the left endpoint is open, so 2 belongs to A′. The number 7 is included in A because the right endpoint is closed, so 7 does not belong to A′. Thus A′ = (−∞, 2] ∪ (7, ∞), making option A correct.
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.
