If U = {1,2,3,4,5} and A = {1,2}, what is Aᶜ \ A?
Answer and explanation
Correct answer: {3,4,5}
Relative to U, the complement of A is Aᶜ = {3,4,5}, because these are the elements of U that are not in A. The sets Aᶜ and A are disjoint, so removing A from Aᶜ removes nothing. Consequently, Aᶜ \ A remains {3,4,5}. Thus the result is option A. This also illustrates that subtracting a disjoint set leaves the original set unchanged.
Frequently asked questions
What is the correct answer to this question?
{3,4,5}
Why is this the correct answer?
Relative to U, the complement of A is Aᶜ = {3,4,5}, because these are the elements of U that are not in A. The sets Aᶜ and A are disjoint, so removing A from Aᶜ removes nothing. Consequently, Aᶜ \ A remains {3,4,5}. Thus the result is option A. This also illustrates that subtracting a disjoint set leaves the original set unchanged.
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.
