If U = {x : x ∈ Z, 0 ≤ x ≤ 10} and A = {0, 2, 4, 6, 8, 10}, what is A'?
Answer and explanation
Correct answer: {1, 3, 5, 7, 9}
The universal set consists of all integers from 0 through 10: U = {0,1,2,3,4,5,6,7,8,9,10}. The complement A' contains elements of U that are not in A. Since A contains all the even integers in this range, the remaining elements are the odd integers {1,3,5,7,9}. Thus A' = {1,3,5,7,9}, so option A is correct. Zero cannot appear in A' because it already belongs to A.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 7, 9}
Why is this the correct answer?
The universal set consists of all integers from 0 through 10: U = {0,1,2,3,4,5,6,7,8,9,10}. The complement A' contains elements of U that are not in A. Since A contains all the even integers in this range, the remaining elements are the odd integers {1,3,5,7,9}. Thus A' = {1,3,5,7,9}, so option A is correct. Zero cannot appear in A' because it already belongs to A.
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.
