1. **State the problem:** We are given a Venn diagram with universal set $U$ and two subsets $A$ and $B$. The numbers in the regions are: - Only in $A$: 32 - In both $A$ and $B$: 7 - Only in $B$: 24 - Outside both $A$ and $B$: 40 We need to find the number of elements in the complement of $A$, denoted $A'$, which means all elements not in $A$. 2. **Formula and rules:** The complement of $A$ is defined as: $$ A' = U - A $$ where $n(A') = n(U) - n(A)$. 3. **Calculate $n(A)$:** $$ n(A) = \text{only in } A + \text{in both } A \text{ and } B = 32 + 7 = 39 $$ 4. **Calculate $n(U)$:** $$ n(U) = 32 + 7 + 24 + 40 = 103 $$ 5. **Calculate $n(A')$:** $$ n(A') = n(U) - n(A) = 103 - 39 = 64 $$ **Final answer:** $$ \boxed{64} $$