Let U = {1,2,3,…,12} and A = {x ∈ U : x is divisible by 4}. What is the complement A′ of A with respect to U?
Answer and explanation
Correct answer: {1,2,3,5,6,7,9,10,11}
The multiples of 4 in U are 4, 8, and 12, so A = {4,8,12}. The complement contains all members of U that are not in A. Removing these three elements from U gives A′ = {1,2,3,5,6,7,9,10,11}. Notice that the complement includes even numbers such as 2, 6, and 10 because they are not divisible by 4.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,5,6,7,9,10,11}
Why is this the correct answer?
The multiples of 4 in U are 4, 8, and 12, so A = {4,8,12}. The complement contains all members of U that are not in A. Removing these three elements from U gives A′ = {1,2,3,5,6,7,9,10,11}. Notice that the complement includes even numbers such as 2, 6, and 10 because they are not divisible by 4.
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.
