By De Morgan’s law, what is (A∪B∪C)ᶜ equal to?
Answer and explanation
Correct answer: Aᶜ∩Bᶜ∩Cᶜ
De Morgan’s law states that the complement of a union equals the intersection of the complements. Applying it successively gives (A∪B∪C)ᶜ = Aᶜ∩Bᶜ∩Cᶜ. In words, an element is outside the union exactly when it is outside A, outside B, and outside C simultaneously. Option A incorrectly uses a union of complements, while C and D omit the required complementation. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
Aᶜ∩Bᶜ∩Cᶜ
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 successively gives (A∪B∪C)ᶜ = Aᶜ∩Bᶜ∩Cᶜ. In words, an element is outside the union exactly when it is outside A, outside B, and outside C simultaneously. Option A incorrectly uses a union of complements, while C and D omit the required complementation. Therefore, option B is correct.
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.
