If Aᶜ = U, which statement about A is correct?
Answer and explanation
Correct answer: A = ∅
Since Aᶜ = U − A, the complement can equal the entire universal set only when A contains no elements. Thus A must be the empty set, ∅. Equivalently, the complement of ∅ is U. Option A would give an empty complement, while A ∪ U is always U, so option D cannot be true for a nonempty universal set. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
Since Aᶜ = U − A, the complement can equal the entire universal set only when A contains no elements. Thus A must be the empty set, ∅. Equivalently, the complement of ∅ is U. Option A would give an empty complement, while A ∪ U is always U, so option D cannot be true for a nonempty universal set. Therefore option B 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.
