If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 3, 5, 7}, what is (A')'?
Answer and explanation
Correct answer: {1, 3, 5, 7}
The complement is always taken relative to U. Here A' = U − A = {2, 4, 6, 8}. Taking the complement of A' removes these even elements from U and returns the odd elements: (A')' = U − A' = {1, 3, 5, 7} = A. This is the double-complement law, (A')' = A. Therefore, option B is correct. Option A is only A', not the double complement.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 7}
Why is this the correct answer?
The complement is always taken relative to U. Here A' = U − A = {2, 4, 6, 8}. Taking the complement of A' removes these even elements from U and returns the odd elements: (A')' = U − A' = {1, 3, 5, 7} = A. This is the double-complement law, (A')' = A. Therefore, option B is correct. Option A is only A', not the double complement.
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.
