If U = {1,2,3} and A = ∅, what is Aᶜ?
Answer and explanation
Correct answer: U
The complement of A consists of all elements of U that are not in A. Since A is the empty set, it contains none of the elements 1, 2, or 3. Thus every element of U belongs to Aᶜ, giving Aᶜ = {1,2,3} = U. This is the standard identity ∅ᶜ = U. The other options omit some elements or incorrectly claim that the complement is empty.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
The complement of A consists of all elements of U that are not in A. Since A is the empty set, it contains none of the elements 1, 2, or 3. Thus every element of U belongs to Aᶜ, giving Aᶜ = {1,2,3} = U. This is the standard identity ∅ᶜ = U. The other options omit some elements or incorrectly claim that the complement is empty.
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.
