If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A = {x ∈ U : x divides 12}, what is A′?
Answer and explanation
Correct answer: {5, 7, 8, 9, 10, 11}
The positive divisors of 12 that belong to U are 1, 2, 3, 4, 6, and 12. Hence A = {1, 2, 3, 4, 6, 12}. The complement A′ consists of all elements of U that are not divisors of 12. Removing these divisors from U leaves A′ = {5, 7, 8, 9, 10, 11}. Therefore, option A is correct. Option B lists A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{5, 7, 8, 9, 10, 11}
Why is this the correct answer?
The positive divisors of 12 that belong to U are 1, 2, 3, 4, 6, and 12. Hence A = {1, 2, 3, 4, 6, 12}. The complement A′ consists of all elements of U that are not divisors of 12. Removing these divisors from U leaves A′ = {5, 7, 8, 9, 10, 11}. Therefore, option A is correct. Option B 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.
