If U = {x : x ∈ ℤ, −5 ≤ x ≤ 5} and A = {x : x² ≤ 9}, what is A'?
Answer and explanation
Correct answer: {−5, −4, 4, 5}
Because x is an integer and x² ≤ 9, we have −3 ≤ x ≤ 3. Therefore, A = {−3, −2, −1, 0, 1, 2, 3}. The universal set is U = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. The complement A' consists of every element of U that is not in A. Removing the seven elements of A leaves {−5, −4, 4, 5}. Hence, option A is correct. The complement must always be taken with respect to the stated universal set U.
Frequently asked questions
What is the correct answer to this question?
{−5, −4, 4, 5}
Why is this the correct answer?
Because x is an integer and x² ≤ 9, we have −3 ≤ x ≤ 3. Therefore, A = {−3, −2, −1, 0, 1, 2, 3}. The universal set is U = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. The complement A' consists of every element of U that is not in A. Removing the seven elements of A leaves {−5, −4, 4, 5}. Hence, option A is correct. The complement must always be taken with respect to the stated universal set U.
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.
