By De Morgan’s law, what is \((A\cap B\cap C)^c\) equal to?
Answer and explanation
Correct answer: \(A^c\cup B^c\cup C^c\)
De Morgan’s law states that the complement of an intersection is the union of the individual complements. Therefore, \((A\cap B\cap C)^c=A^c\cup B^c\cup C^c\). An element is outside the intersection if it fails to belong to at least one of the three sets. Hence, option A is the only correct expression.
Frequently asked questions
What is the correct answer to this question?
\(A^c\cup B^c\cup C^c\)
Why is this the correct answer?
De Morgan’s law states that the complement of an intersection is the union of the individual complements. Therefore, \((A\cap B\cap C)^c=A^c\cup B^c\cup C^c\). An element is outside the intersection if it fails to belong to at least one of the three sets. Hence, option A is the only correct expression.
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.
