For any set A, what is n(A ∩ Aᶜ)?
Advertisement
Answer and explanation
Correct answer: 0
Aᶜ consists of the elements of U that are not in A. Consequently, no element can belong to both A and Aᶜ, so their intersection is the empty set: A ∩ Aᶜ = ∅. The empty set has no elements, and therefore n(A ∩ Aᶜ) = n(∅) = 0. Thus option A is correct regardless of the size or nature of A.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Aᶜ consists of the elements of U that are not in A. Consequently, no element can belong to both A and Aᶜ, so their intersection is the empty set: A ∩ Aᶜ = ∅. The empty set has no elements, and therefore n(A ∩ Aᶜ) = n(∅) = 0. Thus option A is correct regardless of the size or nature of A.
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.
Advertisement