If the universal set U = {x ∈ ℤ | -2 ≤ x ≤ 3} and A = {-1, 0, 1}, what is Aᶜ?
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Answer and explanation
Correct answer: {-2, 2, 3}
Because x is an integer and -2 ≤ x ≤ 3, the universal set is U = {-2, -1, 0, 1, 2, 3}. The complement Aᶜ contains the elements of U that are absent from A. Removing {-1, 0, 1} from U leaves {-2, 2, 3}. Therefore, Aᶜ = {-2, 2, 3}; option B is A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{-2, 2, 3}
Why is this the correct answer?
Because x is an integer and -2 ≤ x ≤ 3, the universal set is U = {-2, -1, 0, 1, 2, 3}. The complement Aᶜ contains the elements of U that are absent from A. Removing {-1, 0, 1} from U leaves {-2, 2, 3}. Therefore, Aᶜ = {-2, 2, 3}; option B is A itself, not its complement.
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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