Let U = {x : x ∈ ℤ, -4 ≤ x ≤ 4} and A = {x : x² ≤ 4}. What is the complement Aᶜ of A with respect to U?
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Answer and explanation
Correct answer: {-4, -3, 3, 4}
The condition x² ≤ 4 is equivalent to -2 ≤ x ≤ 2. Because x must be an integer, A = {-2, -1, 0, 1, 2}. The universal set contains every integer from -4 through 4: {-4, -3, -2, -1, 0, 1, 2, 3, 4}. The elements of U that are absent from A are -4, -3, 3, and 4. Hence Aᶜ = {-4, -3, 3, 4}.
Frequently asked questions
What is the correct answer to this question?
{-4, -3, 3, 4}
Why is this the correct answer?
The condition x² ≤ 4 is equivalent to -2 ≤ x ≤ 2. Because x must be an integer, A = {-2, -1, 0, 1, 2}. The universal set contains every integer from -4 through 4: {-4, -3, -2, -1, 0, 1, 2, 3, 4}. The elements of U that are absent from A are -4, -3, 3, and 4. Hence Aᶜ = {-4, -3, 3, 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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