If the complement of set A with respect to the universal set U is Aᶜ = ∅, which statement about A is correct?
Answer and explanation
Correct answer: A = U
The complement is defined by Aᶜ = U − A. If Aᶜ is empty, there is no element of U outside A. Therefore A must contain every element of U, which means A = U. Option A would make the complement equal to U, not empty. Also, A ∩ U = A, so option D would be empty only if A itself were empty. Hence option B is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
A = U
Why is this the correct answer?
The complement is defined by Aᶜ = U − A. If Aᶜ is empty, there is no element of U outside A. Therefore A must contain every element of U, which means A = U. Option A would make the complement equal to U, not empty. Also, A ∩ U = A, so option D would be empty only if A itself were empty. Hence option B 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.
