If A ⊆ U, which is the most correct definition of A′?
Answer and explanation
Correct answer: A′ = {x : x ∈ U and x ∉ A}
The complement of A is defined relative to the universal set U. It consists of every element that belongs to U but does not belong to A, written as A′ = U \ A or A′ = {x : x ∈ U and x ∉ A}. The condition x ∈ U is essential; without it, the set could include elements outside the stated universe. Therefore option A is the precise definition.
Frequently asked questions
What is the correct answer to this question?
A′ = {x : x ∈ U and x ∉ A}
Why is this the correct answer?
The complement of A is defined relative to the universal set U. It consists of every element that belongs to U but does not belong to A, written as A′ = U \ A or A′ = {x : x ∈ U and x ∉ A}. The condition x ∈ U is essential; without it, the set could include elements outside the stated universe. Therefore option A is the precise definition.
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.
