If U = {1, 2, 3, 4, 5, 6} and A = {1, 6}, what is A' ∩ A?
Answer and explanation
Correct answer: ∅
The complement of A with respect to U is A' = U − A = {2, 3, 4, 5}. The set A contains {1, 6}, so A and A' have no common elements. Therefore, their intersection is empty: A' ∩ A = ∅. This is also the standard complement identity A ∩ A' = ∅. Option B is A' itself, not its intersection with A, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement of A with respect to U is A' = U − A = {2, 3, 4, 5}. The set A contains {1, 6}, so A and A' have no common elements. Therefore, their intersection is empty: A' ∩ A = ∅. This is also the standard complement identity A ∩ A' = ∅. Option B is A' itself, not its intersection with A, so option C 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.
