With respect to the universal set U, which of the following De Morgan identities is true for every pair of sets A and B?
Answer and explanation
Correct answer: (A ∪ B)' = A' ∩ B'
De Morgan’s law states that the complement of a union is the intersection of the complements: (A ∪ B)' = A' ∩ B'. An element belongs to the left side precisely when it belongs to neither A nor B, which means it belongs to both A' and B'. Option A is incorrect because (A ∩ B)' = A' ∪ B', not A' ∩ B'. Also, the double-complement law gives (A')' = A, not A'.
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 a union is the intersection of the complements: (A ∪ B)' = A' ∩ B'. An element belongs to the left side precisely when it belongs to neither A nor B, which means it belongs to both A' and B'. Option A is incorrect because (A ∩ B)' = A' ∪ B', not A' ∩ B'. Also, the double-complement law gives (A')' = A, not 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.
