If A = {a, b, c, d}, B = {b, d, e}, and C = {d, e, f}, what is (A \ B) ∪ (B ∩ C)?
Answer and explanation
Correct answer: {a, c, d, e}
First find the difference A \ B: remove from A every element that is also in B. Since b and d are common to A and B, A \ B = {a, c}. Next find B ∩ C, the elements common to both B and C: B ∩ C = {d, e}. Taking the union combines all distinct elements from these two sets, giving {a, c, d, e}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{a, c, d, e}
Why is this the correct answer?
First find the difference A \ B: remove from A every element that is also in B. Since b and d are common to A and B, A \ B = {a, c}. Next find B ∩ C, the elements common to both B and C: B ∩ C = {d, e}. Taking the union combines all distinct elements from these two sets, giving {a, c, d, e}. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
