1. **State the problem:** We are given a universal set $U$ with two subsets $A$ and $B$ represented in a Venn diagram. The numbers in each region are: - $A$ only: 34 - $B$ only: 37 - Intersection $A \cap B$: 9 - Outside both $A$ and $B$ but inside $U$: 40 We need to find $n(A')$, the number of elements in the complement of $A$ (elements not in $A$). 2. **Recall the formula:** $$n(A') = n(U) - n(A)$$ where $n(U)$ is the total number of elements in the universal set, and $n(A)$ is the number of elements in set $A$. 3. **Calculate $n(A)$:** $$n(A) = n(\text{A only}) + n(A \cap B) = 34 + 9 = 43$$ 4. **Calculate $n(U)$:** $$n(U) = n(\text{A only}) + n(\text{B only}) + n(A \cap B) + n(\text{outside both}) = 34 + 37 + 9 + 40 = 120$$ 5. **Calculate $n(A')$:** $$n(A') = n(U) - n(A) = 120 - 43 = 77$$ **Final answer:** $$\boxed{77}$$