What is (A ∪ B′)′ equal to?
Answer and explanation
Correct answer: A′ ∩ B
Use De Morgan’s law together with the double-complement law. The complement of a union is the intersection of the complements, so (A ∪ B')' = A' ∩ (B')'. Since (B')' = B, the expression simplifies to A' ∩ B. Thus option A is correct. Option B uses a union instead of the required intersection, option C fails to complement A, and option D does not apply the outer complement.
Frequently asked questions
What is the correct answer to this question?
A′ ∩ B
Why is this the correct answer?
Use De Morgan’s law together with the double-complement law. The complement of a union is the intersection of the complements, so (A ∪ B')' = A' ∩ (B')'. Since (B')' = B, the expression simplifies to A' ∩ B. Thus option A is correct. Option B uses a union instead of the required intersection, option C fails to complement A, and option D does not apply the outer complement.
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.
