What is the best test to check whether a given set B is the complement of A?
Answer and explanation
Correct answer: A ∩ B = ∅ and A ∪ B = U
For B to be the complement of A in the universal set U, A and B must satisfy two conditions. First, they must be disjoint, so A ∩ B = ∅. Second, together they must contain every element of U, so A ∪ B = U. These conditions ensure that B contains exactly the elements of U that are outside A. Therefore, option A is the correct test.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅ and A ∪ B = U
Why is this the correct answer?
For B to be the complement of A in the universal set U, A and B must satisfy two conditions. First, they must be disjoint, so A ∩ B = ∅. Second, together they must contain every element of U, so A ∪ B = U. These conditions ensure that B contains exactly the elements of U that are outside A. Therefore, option A is the correct test.
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.
