If the universal set U = {1, 2, 3, 4, 5, 6} and A = {2, 4}, what is A′ − A?
Answer and explanation
Correct answer: {1, 3, 5, 6}
The governing definitions are A′ = U − A and X − Y = the elements in X that are not in Y. First, A′ = {1, 3, 5, 6}, because these are the elements of U outside A = {2, 4}. A set and its complement are disjoint, so none of the elements of A′ is removed when A is subtracted. Therefore A′ − A = A′ = {1, 3, 5, 6}. Option B is A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 6}
Why is this the correct answer?
The governing definitions are A′ = U − A and X − Y = the elements in X that are not in Y. First, A′ = {1, 3, 5, 6}, because these are the elements of U outside A = {2, 4}. A set and its complement are disjoint, so none of the elements of A′ is removed when A is subtracted. Therefore A′ − A = A′ = {1, 3, 5, 6}. Option B is A itself, not its 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.
