How many elements are in A ∪ B?

• A. 6
• B. 3
• C. 5
• D. 4

Answer: (D)

The key idea is that the union A ∪ B counts every distinct element that appears in either set, without double-counting elements that are in both. To find how many elements that is, use the inclusion-exclusion principle: the size of the union equals the size of A plus the size of B minus the size of their intersection.

Think of it this way with a small example: if A has 3 elements and B has 2 elements, and they share one element, then the union has 3 + 2 − 1 = 4 distinct elements. This shows how overlap reduces the total count, because the overlapping item would otherwise be counted twice.

So, the union has four elements because the total unique items contained in either set amount to four after accounting for any overlap. If the overlap were different, the count would change accordingly, but in this case four is the correct total.