If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x ∈ U : x ≤ 4}, which is the most correct form of A′?
Answer and explanation
Correct answer: A′ = {x ∈ U : x > 4}
The condition x ≤ 4 describes the elements 1, 2, 3, and 4, so A = {1, 2, 3, 4}. The complement contains the remaining elements of U: {5, 6, 7, 8, 9, 10}. These are exactly the elements satisfying x > 4. The equality case x = 4 must be excluded from the complement because 4 already belongs to A; therefore option A is the only correct form.
Frequently asked questions
What is the correct answer to this question?
A′ = {x ∈ U : x > 4}
Why is this the correct answer?
The condition x ≤ 4 describes the elements 1, 2, 3, and 4, so A = {1, 2, 3, 4}. The complement contains the remaining elements of U: {5, 6, 7, 8, 9, 10}. These are exactly the elements satisfying x > 4. The equality case x = 4 must be excluded from the complement because 4 already belongs to A; therefore option A is the only correct form.
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.
