If U = {x : x ∈ N, 1 ≤ x ≤ 10} and A = {x : x is even}, what is the complement Aᶜ with respect to U?
Answer and explanation
Correct answer: {1, 3, 5, 7, 9}
Since U contains the natural numbers from 1 through 10, we can write U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The even elements form A = {2, 4, 6, 8, 10}. The complement contains the elements of U that are not even; these are precisely the odd numbers {1, 3, 5, 7, 9}. Hence Aᶜ = {1, 3, 5, 7, 9}, making option A correct. The answer depends on the stated universal set.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 7, 9}
Why is this the correct answer?
Since U contains the natural numbers from 1 through 10, we can write U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The even elements form A = {2, 4, 6, 8, 10}. The complement contains the elements of U that are not even; these are precisely the odd numbers {1, 3, 5, 7, 9}. Hence Aᶜ = {1, 3, 5, 7, 9}, making option A correct. The answer depends on the stated universal set.
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.
