For subsets A and B of a universal set U, which of the following statements is always true?
Answer and explanation
Correct answer: (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ
De Morgan’s first law states that the complement of a union is the intersection of the complements: (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ. An element is outside A ∪ B precisely when it is outside A and also outside B. Option B incorrectly retains the union sign, option C uses the wrong operation, and option D is false because (Aᶜ)ᶜ = A.
Frequently asked questions
What is the correct answer to this question?
(A ∪ B)ᶜ = Aᶜ ∩ Bᶜ
Why is this the correct answer?
De Morgan’s first law states that the complement of a union is the intersection of the complements: (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ. An element is outside A ∪ B precisely when it is outside A and also outside B. Option B incorrectly retains the union sign, option C uses the wrong operation, and option D is false because (Aᶜ)ᶜ = A.
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.
