If A = {a, b, c, d}, B = {b, d, f}, and C = {d, e, f}, what is A ∩ (B ∪ C)?
Answer and explanation
Correct answer: {b, d}
Use the order of operations for sets: calculate the union inside the parentheses first. B ∪ C = {b, d, e, f}. Now intersect this set with A = {a, b, c, d}; only elements appearing in both sets are retained. Those common elements are b and d. Hence A ∩ (B ∪ C) = {b, d}, so option A is correct. The other options either omit common elements or include elements not in A.
Frequently asked questions
What is the correct answer to this question?
{b, d}
Why is this the correct answer?
Use the order of operations for sets: calculate the union inside the parentheses first. B ∪ C = {b, d, e, f}. Now intersect this set with A = {a, b, c, d}; only elements appearing in both sets are retained. Those common elements are b and d. Hence A ∩ (B ∪ C) = {b, d}, so option A is correct. The other options either omit common elements or include elements not in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
