If U = {x : x ∈ ℕ, x ≤ 12} and A = {x ∈ U : x is not divisible by 2}, what is Aᶜ?
Answer and explanation
Correct answer: {2, 4, 6, 8, 10, 12}
Taking ℕ here as the positive natural numbers, U = {1, 2, 3, …, 12}. Numbers not divisible by 2 are the odd numbers, so A = {1, 3, 5, 7, 9, 11}. The complement contains the remaining elements of U, namely the even numbers {2, 4, 6, 8, 10, 12}. Therefore option B is correct; option A lists A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{2, 4, 6, 8, 10, 12}
Why is this the correct answer?
Taking ℕ here as the positive natural numbers, U = {1, 2, 3, …, 12}. Numbers not divisible by 2 are the odd numbers, so A = {1, 3, 5, 7, 9, 11}. The complement contains the remaining elements of U, namely the even numbers {2, 4, 6, 8, 10, 12}. Therefore option B is correct; option A lists A itself, not its complement.
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.
