If A ∪ B = ∅, what is A' ∩ B' equal to?
Answer and explanation
Correct answer: U
If the union of A and B is empty, neither set can contain any element; otherwise that element would belong to their union. Thus A = ∅ and B = ∅. Their complements relative to the universal set U are both U. Consequently A' ∩ B' = U ∩ U = U. This also follows directly from De Morgan’s law: A' ∩ B' = (A ∪ B)' = ∅' = U. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
If the union of A and B is empty, neither set can contain any element; otherwise that element would belong to their union. Thus A = ∅ and B = ∅. Their complements relative to the universal set U are both U. Consequently A' ∩ B' = U ∩ U = U. This also follows directly from De Morgan’s law: A' ∩ B' = (A ∪ B)' = ∅' = U. Therefore option A is correct.
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.
