If A ∪ A′ = U and A ∩ A′ = ∅, what kind of set is A′ with respect to A?
Answer and explanation
Correct answer: The complement of A
A set and its complement have two defining properties: their union is the universal set, and their intersection is empty. The equations A ∪ A′ = U and A ∩ A′ = ∅ state exactly these properties. Thus A′ contains every element of U that is not in A, so A′ is the complement of A. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
The complement of A
Why is this the correct answer?
A set and its complement have two defining properties: their union is the universal set, and their intersection is empty. The equations A ∪ A′ = U and A ∩ A′ = ∅ state exactly these properties. Thus A′ contains every element of U that is not in A, so A′ is the complement of A. Therefore, option C is correct.
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.
