If U = {x : x ∈ Z, −9 ≤ x ≤ 9} and A = {x : x ∈ U, |x| > 4}, what is A′?
Answer and explanation
Correct answer: {−4, −3, −2, −1, 0, 1, 2, 3, 4}
The universal set contains every integer from −9 to 9. Set A consists of integers whose absolute value is greater than 4, namely −9 through −5 and 5 through 9. Its complement therefore contains the integers in U that do not satisfy |x| > 4. The opposite condition is |x| ≤ 4, which gives −4, −3, −2, −1, 0, 1, 2, 3, and 4. Hence option A is correct; option B describes A itself.
Frequently asked questions
What is the correct answer to this question?
{−4, −3, −2, −1, 0, 1, 2, 3, 4}
Why is this the correct answer?
The universal set contains every integer from −9 to 9. Set A consists of integers whose absolute value is greater than 4, namely −9 through −5 and 5 through 9. Its complement therefore contains the integers in U that do not satisfy |x| > 4. The opposite condition is |x| ≤ 4, which gives −4, −3, −2, −1, 0, 1, 2, 3, and 4. Hence option A is correct; option B describes A itself.
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.
