1. The problem asks for the number of elements in the union of sets A and B, denoted as $n(A \cup B)$. This means we want to find how many elements are in either set A, set B, or both. 2. The formula for the union of two sets is: $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$ This formula adds the number of elements in A and B but subtracts the intersection once to avoid double counting. 3. From the Venn diagram: - Elements only in A: 30 - Elements only in B: 22 - Elements in both A and B (intersection): 13 - Elements outside both sets: 40 (not needed for union calculation) 4. Calculate $n(A)$ and $n(B)$: $$n(A) = 30 + 13 = 43$$ $$n(B) = 22 + 13 = 35$$ 5. Apply the union formula: $$n(A \cup B) = 43 + 35 - 13$$ 6. Simplify the expression: $$n(A \cup B) = 78 - 13 = 65$$ 7. Therefore, the number of elements in $A \cup B$ is 65.