With respect to a universal set, which statement correctly represents De Morgan's law for three sets?
Answer and explanation
Correct answer: \((A\cup B\cup C)'=A'\cap B'\cap C'\)
De Morgan's law states that the complement of a union equals the intersection of the complements. Applying it to three sets gives \((A\cup B\cup C)'=A'\cap B'\cap C'\). An element is outside the union exactly when it is outside A, outside B, and outside C simultaneously. Therefore option A is correct. Option B fails to interchange union and intersection, while option C incorrectly gives the complement of an intersection.
Frequently asked questions
What is the correct answer to this question?
\((A\cup B\cup C)'=A'\cap B'\cap C'\)
Why is this the correct answer?
De Morgan's law states that the complement of a union equals the intersection of the complements. Applying it to three sets gives \((A\cup B\cup C)'=A'\cap B'\cap C'\). An element is outside the union exactly when it is outside A, outside B, and outside C simultaneously. Therefore option A is correct. Option B fails to interchange union and intersection, while option C incorrectly gives the complement of an 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.
