If U = {1, 2, 3, 4, 5} and A = {1, 5}, what is (A')'?
Answer and explanation
Correct answer: {1, 5}
The complement of A in U is A' = U − A = {2, 3, 4}. Taking the complement once more gives (A')' = U − {2, 3, 4} = {1, 5}, which is the original set A. This illustrates the double-complement law: the complement of a complement returns the original set, provided the same universal set is used. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 5}
Why is this the correct answer?
The complement of A in U is A' = U − A = {2, 3, 4}. Taking the complement once more gives (A')' = U − {2, 3, 4} = {1, 5}, which is the original set A. This illustrates the double-complement law: the complement of a complement returns the original set, provided the same universal set is used. Hence option A 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.
