If U = ℝ and A = {x ∈ ℝ : x ≤ −1 or x > 3}, what is A′?
Answer and explanation
Correct answer: (-1,3]
The set A contains every real number less than or equal to −1 and every real number greater than 3. Its complement therefore consists of real numbers greater than −1 and less than or equal to 3. The point −1 is excluded because it belongs to A, while 3 is included because the condition x > 3 excludes it from A. Hence A′ = (-1,3].
Frequently asked questions
What is the correct answer to this question?
(-1,3]
Why is this the correct answer?
The set A contains every real number less than or equal to −1 and every real number greater than 3. Its complement therefore consists of real numbers greater than −1 and less than or equal to 3. The point −1 is excluded because it belongs to A, while 3 is included because the condition x > 3 excludes it from A. Hence A′ = (-1,3].
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.
