According to De Morgan's law, what is (A ∪ B)ᶜ equal to?
Answer and explanation
Correct answer: Aᶜ ∩ Bᶜ
An element belongs to (A ∪ B)ᶜ when it does not belong to the union A ∪ B. Not belonging to a union means that the element belongs to neither A nor B. Therefore, it must belong to both complements Aᶜ and Bᶜ. Hence De Morgan's law gives (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ. The union and intersection are interchanged when a complement is distributed. Option B instead represents (A ∩ B)ᶜ.
Frequently asked questions
What is the correct answer to this question?
Aᶜ ∩ Bᶜ
Why is this the correct answer?
An element belongs to (A ∪ B)ᶜ when it does not belong to the union A ∪ B. Not belonging to a union means that the element belongs to neither A nor B. Therefore, it must belong to both complements Aᶜ and Bᶜ. Hence De Morgan's law gives (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ. The union and intersection are interchanged when a complement is distributed. Option B instead represents (A ∩ B)ᶜ.
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.
