If the universal set is U = {a, b, c, d, e, f}, A = {a, c, e}, and B = {b, d, f}, which of the following statements is correct?
Answer and explanation
Correct answer: B = Aᶜ
The complement Aᶜ contains all elements of U that are absent from A. Since A = {a, c, e}, removing these elements from U = {a, b, c, d, e, f} leaves {b, d, f}. This remaining set is exactly B. Hence Aᶜ = {b, d, f} = B, so statement A is correct. In fact, A and B are disjoint and their union is U, which confirms that they are complements.
Frequently asked questions
What is the correct answer to this question?
B = Aᶜ
Why is this the correct answer?
The complement Aᶜ contains all elements of U that are absent from A. Since A = {a, c, e}, removing these elements from U = {a, b, c, d, e, f} leaves {b, d, f}. This remaining set is exactly B. Hence Aᶜ = {b, d, f} = B, so statement A is correct. In fact, A and B are disjoint and their union is U, which confirms that they are complements.
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.
