Let U = {x : x ∈ Z, −3 ≤ x ≤ 3} and A = {x : x ≥ 0}. What is the complement A' with respect to U?
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Answer and explanation
Correct answer: {−3, −2, −1}
Because x is an integer and −3 ≤ x ≤ 3, the universal set is U = {−3, −2, −1, 0, 1, 2, 3}. The condition x ≥ 0 selects A = {0, 1, 2, 3}. The complement A' consists of every element of U that is not in A. Hence A' = {−3, −2, −1}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{−3, −2, −1}
Why is this the correct answer?
Because x is an integer and −3 ≤ x ≤ 3, the universal set is U = {−3, −2, −1, 0, 1, 2, 3}. The condition x ≥ 0 selects A = {0, 1, 2, 3}. The complement A' consists of every element of U that is not in A. Hence A' = {−3, −2, −1}, so option A is correct.
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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