If A' ∪ B' = U, what conclusion is correct about A ∩ B?
Answer and explanation
Correct answer: A ∩ B = ∅
Apply De Morgan's law to the left side: A' ∪ B' = (A ∩ B)'. The condition says that (A ∩ B)' is the entire universal set U. The only subset whose complement is U is the empty set, because no element can belong to A ∩ B. Hence A ∩ B = ∅. This means A and B are disjoint, although it does not imply that either set itself is empty.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
Apply De Morgan's law to the left side: A' ∪ B' = (A ∩ B)'. The condition says that (A ∩ B)' is the entire universal set U. The only subset whose complement is U is the empty set, because no element can belong to A ∩ B. Hence A ∩ B = ∅. This means A and B are disjoint, although it does not imply that either set itself is empty.
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.
