If U = R and A = {x | x ≤ 1 or x > 9}, what is A'?
Answer and explanation
Correct answer: (1, 9]
The set A contains all real numbers satisfying x ≤ 1 or x > 9. To find its complement, both conditions must fail simultaneously: x > 1 and x ≤ 9. Their intersection is the interval (1, 9]. The number 1 is excluded because it is already in A, while 9 is included because A contains only numbers strictly greater than 9. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
(1, 9]
Why is this the correct answer?
The set A contains all real numbers satisfying x ≤ 1 or x > 9. To find its complement, both conditions must fail simultaneously: x > 1 and x ≤ 9. Their intersection is the interval (1, 9]. The number 1 is excluded because it is already in A, while 9 is included because A contains only numbers strictly greater than 9. Hence 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.
