If the universal set U = [1, 9] and A = [1, 5), what is Aᶜ with respect to U?
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Answer and explanation
Correct answer: [5, 9]
The complement is taken relative to U, so Aᶜ = U \ A. The interval A = [1, 5) contains 1 and all numbers up to but not including 5. Therefore, 5 is excluded from A and included in its complement. The endpoint 9 is included in U, and A contains no numbers beyond 5, so 9 remains included. Thus Aᶜ = [5, 9].
Frequently asked questions
What is the correct answer to this question?
[5, 9]
Why is this the correct answer?
The complement is taken relative to U, so Aᶜ = U \ A. The interval A = [1, 5) contains 1 and all numbers up to but not including 5. Therefore, 5 is excluded from A and included in its complement. The endpoint 9 is included in U, and A contains no numbers beyond 5, so 9 remains included. Thus Aᶜ = [5, 9].
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.
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