If A = {a, b, c, e}, B = {b, d, e}, and C = {e, f}, what is (A ∪ B) ∩ (B ∪ C)?
Answer and explanation
Correct answer: {b, d, e}
Use the definitions of union and intersection systematically. First, A ∪ B = {a, b, c, d, e}, because all distinct elements from both sets are included. Next, B ∪ C = {b, d, e, f}. The common elements in these two unions are b, d, and e. Hence (A ∪ B) ∩ (B ∪ C) = {b, d, e}. Option A is correct; option D is the full union, not the intersection.
Frequently asked questions
What is the correct answer to this question?
{b, d, e}
Why is this the correct answer?
Use the definitions of union and intersection systematically. First, A ∪ B = {a, b, c, d, e}, because all distinct elements from both sets are included. Next, B ∪ C = {b, d, e, f}. The common elements in these two unions are b, d, and e. Hence (A ∪ B) ∩ (B ∪ C) = {b, d, e}. Option A is correct; option D is the full union, not the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
