Which option gives the correct form of \((A\cup B)'\)?
Answer and explanation
Correct answer: \(A'\cap B'\)
De Morgan’s law states that the complement of a union is the intersection of the complements. Thus, \((A\cup B)'=A'\cap B'\). An element is outside \(A\cup B\) only when it is outside both \(A\) and \(B\), which explains the intersection symbol. Therefore, option A is correct. Option B incorrectly uses a union, and options C and D do not complement both original sets correctly.
Frequently asked questions
What is the correct answer to this question?
\(A'\cap B'\)
Why is this the correct answer?
De Morgan’s law states that the complement of a union is the intersection of the complements. Thus, \((A\cup B)'=A'\cap B'\). An element is outside \(A\cup B\) only when it is outside both \(A\) and \(B\), which explains the intersection symbol. Therefore, option A is correct. Option B incorrectly uses a union, and options C and D do not complement both original sets correctly.
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.
