Which set has a complement equal to the universal set U?
Answer and explanation
Correct answer: The empty set ∅
By definition, the complement of a set A contains all elements of U that are not in A. If A is the empty set, it contains no elements, so every element of U lies outside A. Therefore, ∅ᶜ = U. The complement of U is instead ∅, and a singleton or infinite set generally has a complement that is neither necessarily empty nor the whole universal set. Hence option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
The empty set ∅
Why is this the correct answer?
By definition, the complement of a set A contains all elements of U that are not in A. If A is the empty set, it contains no elements, so every element of U lies outside A. Therefore, ∅ᶜ = U. The complement of U is instead ∅, and a singleton or infinite set generally has a complement that is neither necessarily empty nor the whole universal set. Hence option A is the unique correct answer.
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.
