Which statement is true about the sets A = {1,2,3} and B = {3,4}?

Which statement is true about the sets A = {1,2,3} and B = {3,4}?

• A. A ∪ B has 3 elements, and A ∩ B has 1 element
• B. A ∪ B has 4 elements, and A ∩ B has 0 elements
• C. A ∪ B has 4 elements, and A ∩ B has 1 element
• D. A ∪ B has 5 elements, and A ∩ B has 0 elements

Answer: (C)

The key idea is how union and intersection count elements. The union of two sets combines all distinct elements that appear in either set, while the intersection only includes elements that appear in both. For A = {1, 2, 3} and B = {3, 4}, the union is {1, 2, 3, 4}, which has four elements. The intersection is {3}, which has one element. So the description “A ∪ B has 4 elements, and A ∩ B has 1 element” is correct—the counts match exactly. The other descriptions don’t fit because they misstate these counts: the union isn’t only three elements and the intersection isn’t zero; and the union isn’t five elements.

The key idea is how union and intersection count elements. The union of two sets combines all distinct elements that appear in either set, while the intersection only includes elements that appear in both.

For A = {1, 2, 3} and B = {3, 4}, the union is {1, 2, 3, 4}, which has four elements. The intersection is {3}, which has one element. So the description “A ∪ B has 4 elements, and A ∩ B has 1 element” is correct—the counts match exactly.

The other descriptions don’t fit because they misstate these counts: the union isn’t only three elements and the intersection isn’t zero; and the union isn’t five elements.