Let U = {x ∈ ℤ | −4 ≤ x ≤ 6} and A = {x ∈ U | (x − 1)(x + 2) ≥ 0}. What is A′, the complement of A with respect to U?
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Answer and explanation
Correct answer: {−1, 0}
First solve the inequality (x − 1)(x + 2) ≥ 0. Its critical values are −2 and 1, so the product is non-negative when x ≤ −2 or x ≥ 1. Restricting to U gives A = {−4, −3, −2, 1, 2, 3, 4, 5, 6}. Therefore, the elements of U not in A are −1 and 0. Hence A′ = {−1, 0}.
Frequently asked questions
What is the correct answer to this question?
{−1, 0}
Why is this the correct answer?
First solve the inequality (x − 1)(x + 2) ≥ 0. Its critical values are −2 and 1, so the product is non-negative when x ≤ −2 or x ≥ 1. Restricting to U gives A = {−4, −3, −2, 1, 2, 3, 4, 5, 6}. Therefore, the elements of U not in A are −1 and 0. Hence A′ = {−1, 0}.
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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