If the universal set is U = ℝ and A = {x : x ≤ −1 or x > 4}, what is A′?
Answer and explanation
Correct answer: (−1, 4]
The set A contains all real numbers satisfying x ≤ −1 or x > 4. Its complement must satisfy the opposite of both conditions simultaneously: x > −1 and x ≤ 4. Therefore A′ = {x : −1 < x ≤ 4} = (−1, 4]. The endpoint −1 is excluded because it belongs to A, while 4 is included because 4 is not greater than 4. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
(−1, 4]
Why is this the correct answer?
The set A contains all real numbers satisfying x ≤ −1 or x > 4. Its complement must satisfy the opposite of both conditions simultaneously: x > −1 and x ≤ 4. Therefore A′ = {x : −1 < x ≤ 4} = (−1, 4]. The endpoint −1 is excluded because it belongs to A, while 4 is included because 4 is not greater than 4. Thus option A is 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.
