If A ∪ Aᶜ is considered, what is its value?
Answer and explanation
Correct answer: U
Every element of the universal set U either belongs to A or does not belong to A. The elements that do not belong to A are exactly the elements of Aᶜ. Thus, together A and Aᶜ contain every element of U, so A ∪ Aᶜ = U. Therefore, option D is correct.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
Every element of the universal set U either belongs to A or does not belong to A. The elements that do not belong to A are exactly the elements of Aᶜ. Thus, together A and Aᶜ contain every element of U, so A ∪ Aᶜ = U. Therefore, option D 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.