For any set A, what is A ∪ Aᶜ equal to?
Answer and explanation
Correct answer: U, the universal set
Every element of the universal set U is either in A or not in A. The elements that are not in A form Aᶜ. Consequently, taking the union of A and Aᶜ includes every element of U and does not include anything outside U, so A ∪ Aᶜ = U. This is called the complement or union law. Option B describes the intersection law, A ∩ Aᶜ = ∅, not the union law.
Frequently asked questions
What is the correct answer to this question?
U, the universal set
Why is this the correct answer?
Every element of the universal set U is either in A or not in A. The elements that are not in A form Aᶜ. Consequently, taking the union of A and Aᶜ includes every element of U and does not include anything outside U, so A ∪ Aᶜ = U. This is called the complement or union law. Option B describes the intersection law, A ∩ Aᶜ = ∅, not the union law.
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.
