For subsets A and B of a universal set U, which statement correctly represents De Morgan’s law?
Answer and explanation
Correct answer: (A ∩ B)' = A' ∪ B'
One of De Morgan’s laws states that the complement of an intersection equals the union of the complements: (A ∩ B)' = A' ∪ B'. The other related law is (A ∪ B)' = A' ∩ B'. Thus, complementation reverses the operation between intersection and union. Option B fails to change the operation, option C uses the wrong operation, and option D contradicts the double-complement law.
Frequently asked questions
What is the correct answer to this question?
(A ∩ B)' = A' ∪ B'
Why is this the correct answer?
One of De Morgan’s laws states that the complement of an intersection equals the union of the complements: (A ∩ B)' = A' ∪ B'. The other related law is (A ∪ B)' = A' ∩ B'. Thus, complementation reverses the operation between intersection and union. Option B fails to change the operation, option C uses the wrong operation, and option D contradicts the double-complement law.
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.
