If B is called the complement of A, which statement must be true?
Answer and explanation
Correct answer: A ∩ B = ∅ and A ∪ B = U
By definition, the complement B = Aᶜ contains every element of the universal set U that is not in A. Therefore A and B have no common element, so A ∩ B = ∅. Together, A and its complement contain every element of U, so A ∪ B = U. These two identities characterize a complement and make option A the only valid statement.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅ and A ∪ B = U
Why is this the correct answer?
By definition, the complement B = Aᶜ contains every element of the universal set U that is not in A. Therefore A and B have no common element, so A ∩ B = ∅. Together, A and its complement contain every element of U, so A ∪ B = U. These two identities characterize a complement and make option A the only valid statement.
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.
