If U = {0, 1, 2, 3, 4, 5}, A = {0, 2, 4}, and B = {1, 3, 5}, what is A′, the complement of A with respect to U?
Answer and explanation
Correct answer: B = {1, 3, 5}
The complement of A relative to U is written A′ = U \ A. It contains every element of the universal set U that is not an element of A. Removing 0, 2, and 4 from U leaves 1, 3, and 5. Therefore A′ = {1, 3, 5}, which is exactly B. A itself contains the removed elements, U contains too many elements, and the empty set contains none.
Frequently asked questions
What is the correct answer to this question?
B = {1, 3, 5}
Why is this the correct answer?
The complement of A relative to U is written A′ = U \ A. It contains every element of the universal set U that is not an element of A. Removing 0, 2, and 4 from U leaves 1, 3, and 5. Therefore A′ = {1, 3, 5}, which is exactly B. A itself contains the removed elements, U contains too many elements, and the empty set contains none.
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.
