If the universal set U = (-3, 4] and A = (-3, 1], what is the complement Aᶜ of A with respect to U?
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Answer and explanation
Correct answer: (1, 4]
The complement Aᶜ consists of elements in U that are not in A, so Aᶜ = U \ A. The number 1 is included in A because the interval ends with a square bracket at 1; therefore, 1 is excluded from Aᶜ. The number 4 is included in U and is not in A, so it remains included. Hence, Aᶜ = (1, 4].
Frequently asked questions
What is the correct answer to this question?
(1, 4]
Why is this the correct answer?
The complement Aᶜ consists of elements in U that are not in A, so Aᶜ = U \ A. The number 1 is included in A because the interval ends with a square bracket at 1; therefore, 1 is excluded from Aᶜ. The number 4 is included in U and is not in A, so it remains included. Hence, Aᶜ = (1, 4].
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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