For any set A, what is A ∩ Aᶜ equal to?
Answer and explanation
Correct answer: ∅, the empty set
The complement Aᶜ contains precisely those elements of the universal set that are not in A. Therefore, no element can belong to both A and Aᶜ at the same time. Their common part is empty, so A ∩ Aᶜ = ∅. This is called the complement or intersection law. Option B belongs to the union identity A ∪ Aᶜ = U, while options C and D incorrectly treat the intersection as one of the two sets.
Frequently asked questions
What is the correct answer to this question?
∅, the empty set
Why is this the correct answer?
The complement Aᶜ contains precisely those elements of the universal set that are not in A. Therefore, no element can belong to both A and Aᶜ at the same time. Their common part is empty, so A ∩ Aᶜ = ∅. This is called the complement or intersection law. Option B belongs to the union identity A ∪ Aᶜ = U, while options C and D incorrectly treat the intersection as one of the two sets.
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.
