If U = {x : x ∈ Z, -3 ≤ x ≤ 6} and A = {x : x ≥ 2}, what is A'?
Answer and explanation
Correct answer: {-3, -2, -1, 0, 1}
A complement must be determined relative to the stated universal set, not relative to all integers. The set U contains the integers −3 through 6. Within U, the condition x ≥ 2 gives A = {2, 3, 4, 5, 6}. Therefore the elements left outside A are −3, −2, −1, 0 and 1. Thus A' = {−3, −2, −1, 0, 1}, which is option A. Option B is A itself, while C and D omit or include boundary elements incorrectly.
Frequently asked questions
What is the correct answer to this question?
{-3, -2, -1, 0, 1}
Why is this the correct answer?
A complement must be determined relative to the stated universal set, not relative to all integers. The set U contains the integers −3 through 6. Within U, the condition x ≥ 2 gives A = {2, 3, 4, 5, 6}. Therefore the elements left outside A are −3, −2, −1, 0 and 1. Thus A' = {−3, −2, −1, 0, 1}, which is option A. Option B is A itself, while C and D omit or include boundary elements incorrectly.
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.
