If \(A\) and \(B\) are subsets of \(U\), what is \((A\cap B)'\) equal to?
Answer and explanation
Correct answer: \(A'\cup B'\)
De Morgan’s law states that the complement of an intersection is the union of the complements: \((A\cap B)'=A'\cup B'\). An element is outside \(A\cap B\) whenever it fails to belong to at least one of the two sets. Therefore it belongs to \(A'\cup B'\). Option B is correct; option A incorrectly uses intersection.
Frequently asked questions
What is the correct answer to this question?
\(A'\cup B'\)
Why is this the correct answer?
De Morgan’s law states that the complement of an intersection is the union of the complements: \((A\cap B)'=A'\cup B'\). An element is outside \(A\cap B\) whenever it fails to belong to at least one of the two sets. Therefore it belongs to \(A'\cup B'\). Option B is correct; option A incorrectly uses intersection.
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.
