Which formula correctly represents the complement of set A?
Answer and explanation
Correct answer: Aᶜ = U \ A
By definition, the complement of A contains elements that are in the universal set U but are not in A. Set difference expresses exactly this idea, so Aᶜ = U \ A. Since A is normally a subset of U, A \ U is empty rather than the complement. Also, A ∩ U equals A, and A ∪ U equals U. Thus only option A has the required meaning.
Frequently asked questions
What is the correct answer to this question?
Aᶜ = U \ A
Why is this the correct answer?
By definition, the complement of A contains elements that are in the universal set U but are not in A. Set difference expresses exactly this idea, so Aᶜ = U \ A. Since A is normally a subset of U, A \ U is empty rather than the complement. Also, A ∩ U equals A, and A ∪ U equals U. Thus only option A has the required meaning.
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.
