If A ∩ B = ∅, what is (A ∪ B)' equal to?
Answer and explanation
Correct answer: A' ∩ B'
De Morgan's law states that the complement of a union equals the intersection of the complements: (A ∪ B)' = A' ∩ B'. This identity is valid whether or not A and B overlap. The given condition A ∩ B = ∅ only tells us that A and B are disjoint; it does not change the De Morgan identity. Therefore, option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
A' ∩ B'
Why is this the correct answer?
De Morgan's law states that the complement of a union equals the intersection of the complements: (A ∪ B)' = A' ∩ B'. This identity is valid whether or not A and B overlap. The given condition A ∩ B = ∅ only tells us that A and B are disjoint; it does not change the De Morgan identity. Therefore, 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.
