Let the universal set be U = [0, 10] and A = [0, 4]. What is the complement Aᶜ of A with respect to U?
Answer and explanation
Correct answer: (4, 10]
For intervals, parentheses exclude an endpoint and brackets include it. The set A = [0,4] contains every real number from 0 through 4, including both endpoints. Its complement within U = [0,10] therefore contains numbers greater than 4 and up to 10. The point 4 is excluded, while 10 is included, giving Aᶜ = (4,10]. Option B incorrectly includes 4, and option C is A itself.
Frequently asked questions
What is the correct answer to this question?
(4, 10]
Why is this the correct answer?
For intervals, parentheses exclude an endpoint and brackets include it. The set A = [0,4] contains every real number from 0 through 4, including both endpoints. Its complement within U = [0,10] therefore contains numbers greater than 4 and up to 10. The point 4 is excluded, while 10 is included, giving Aᶜ = (4,10]. Option B incorrectly includes 4, and option C is A itself.
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.
