If U = {1, 2, 3, 4, 5, 6, 7} and A = {1, 3, 5, 7}, what is A′, the complement of A relative to U?
Answer and explanation
Correct answer: {2, 4, 6}
The complement of A relative to the universal set U contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5, 6, 7}, remove 1, 3, 5, and 7 because these belong to A. The elements left are 2, 4, and 6. Therefore, A′ = U − A = {2, 4, 6}. Option B is A itself, not its complement, while options C and D do not contain exactly all the required elements.
Frequently asked questions
What is the correct answer to this question?
{2, 4, 6}
Why is this the correct answer?
The complement of A relative to the universal set U contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5, 6, 7}, remove 1, 3, 5, and 7 because these belong to A. The elements left are 2, 4, and 6. Therefore, A′ = U − A = {2, 4, 6}. Option B is A itself, not its complement, while options C and D do not contain exactly all the required elements.
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.
