If A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, and C = {1, 4, 7, 8}, what is (A ∪ B) ∩ C?
Answer and explanation
Correct answer: {1, 4, 8}
First find the union of A and B by listing every element that occurs in either set: A ∪ B = {1, 2, 3, 4, 5, 6, 8}. Next, intersect this result with C, which means retain only elements also present in C = {1, 4, 7, 8}. The common elements are 1, 4, and 8. Therefore, (A ∪ B) ∩ C = {1, 4, 8}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 8}
Why is this the correct answer?
First find the union of A and B by listing every element that occurs in either set: A ∪ B = {1, 2, 3, 4, 5, 6, 8}. Next, intersect this result with C, which means retain only elements also present in C = {1, 4, 7, 8}. The common elements are 1, 4, and 8. Therefore, (A ∪ B) ∩ C = {1, 4, 8}, so 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).
