If A = {1, 2, 4, 6}, B = {2, 3, 6, 8}, and C = {2, 6, 9}, what is (A ∪ B) ∩ C?
Answer and explanation
Correct answer: {2, 6}
First form the union of A and B by listing each distinct element once: A ∪ B = {1, 2, 3, 4, 6, 8}. The intersection with C = {2, 6, 9} keeps only elements found in both sets. The common elements are 2 and 6; 9 is not in the union. Therefore, (A ∪ B) ∩ C = {2, 6}, making option B correct. Option A is the union's non-common portion, not the requested intersection.
Frequently asked questions
What is the correct answer to this question?
{2, 6}
Why is this the correct answer?
First form the union of A and B by listing each distinct element once: A ∪ B = {1, 2, 3, 4, 6, 8}. The intersection with C = {2, 6, 9} keeps only elements found in both sets. The common elements are 2 and 6; 9 is not in the union. Therefore, (A ∪ B) ∩ C = {2, 6}, making option B correct. Option A is the union's non-common portion, not the requested 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).
