If A = {2,4,6,8,10}, B = {4,8,12}, and C = {2,8,14}, what is (A ∩ B) ∪ C?
Answer and explanation
Correct answer: {2,4,8,14}
First calculate the intersection A ∩ B. The elements common to A and B are 4 and 8, so A ∩ B = {4,8}. Next take the union with C: {4,8} ∪ {2,8,14} = {2,4,8,14}. Repeated elements are written only once. Therefore option A is correct. Option C omits 4, while option D incorrectly includes elements that are not in the intermediate result.
Frequently asked questions
What is the correct answer to this question?
{2,4,8,14}
Why is this the correct answer?
First calculate the intersection A ∩ B. The elements common to A and B are 4 and 8, so A ∩ B = {4,8}. Next take the union with C: {4,8} ∪ {2,8,14} = {2,4,8,14}. Repeated elements are written only once. Therefore option A is correct. Option C omits 4, while option D incorrectly includes elements that are not in the intermediate result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
