If the universal set is U = {a, b, c, d, e}, A = {a, b, d}, and B = {b, c, d}, what is the complement of A ∩ B with respect to U?
Answer and explanation
Correct answer: {a, c, e}
The intersection contains elements common to both sets. Comparing A and B gives A ∩ B = {b, d}. The complement is formed by removing b and d from the universal set U = {a, b, c, d, e}. The remaining elements are a, c, and e. Hence (A ∩ B)′ = {a, c, e}, so option A is correct. Option B represents the intersection itself.
Frequently asked questions
What is the correct answer to this question?
{a, c, e}
Why is this the correct answer?
The intersection contains elements common to both sets. Comparing A and B gives A ∩ B = {b, d}. The complement is formed by removing b and d from the universal set U = {a, b, c, d, e}. The remaining elements are a, c, and e. Hence (A ∩ B)′ = {a, c, e}, so option A is correct. Option B represents the intersection itself.
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.
