Which of the following statements about the complements of two sets, relative to a universal set, is always true?
Answer and explanation
Correct answer: (A ∩ B)′ = A′ ∪ B′
De Morgan’s law states that the complement of an intersection is the union of the complements: (A ∩ B)′ = A′ ∪ B′. An element fails to belong to A ∩ B whenever it is absent from A or absent from B. Option B is incorrect because (A ∪ B)′ = A′ ∩ B′. Also, (A′)′ = A and A ∪ A′ = U, not the empty set.
Frequently asked questions
What is the correct answer to this question?
(A ∩ B)′ = A′ ∪ B′
Why is this the correct answer?
De Morgan’s law states that the complement of an intersection is the union of the complements: (A ∩ B)′ = A′ ∪ B′. An element fails to belong to A ∩ B whenever it is absent from A or absent from B. Option B is incorrect because (A ∪ B)′ = A′ ∩ B′. Also, (A′)′ = A and A ∪ A′ = U, not the empty set.
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.
