If A ∩ Aᶜ is considered, what is its value?
Answer and explanation
Correct answer: ∅
The complement Aᶜ contains exactly those elements of the universal set U that are not in A. Therefore, an element cannot belong to both A and Aᶜ at the same time. The two sets are disjoint, so their intersection contains no element: A ∩ Aᶜ = ∅. Hence option D is correct; A, Aᶜ, and U represent other set expressions, not this intersection.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement Aᶜ contains exactly those elements of the universal set U that are not in A. Therefore, an element cannot belong to both A and Aᶜ at the same time. The two sets are disjoint, so their intersection contains no element: A ∩ Aᶜ = ∅. Hence option D is correct; A, Aᶜ, and U represent other set expressions, not this intersection.
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.
