If A = {1,2,3,4}, B = {3,4,5}, and C = {4,5,6}, what is (A ∪ B) ∩ C?
Answer and explanation
Correct answer: {4,5}
First form the union A ∪ B by listing every element appearing in either set without repetition: A ∪ B = {1,2,3,4,5}. Now intersect this result with C = {4,5,6}. The common elements are 4 and 5, so (A ∪ B) ∩ C = {4,5}. Therefore option A is correct. Option B includes 3, which is not in C; option D omits 4; and option C is the union of all listed elements rather than the requested intersection.
Frequently asked questions
What is the correct answer to this question?
{4,5}
Why is this the correct answer?
First form the union A ∪ B by listing every element appearing in either set without repetition: A ∪ B = {1,2,3,4,5}. Now intersect this result with C = {4,5,6}. The common elements are 4 and 5, so (A ∪ B) ∩ C = {4,5}. Therefore option A is correct. Option B includes 3, which is not in C; option D omits 4; and option C is the union of all listed elements rather than 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).
