To solve this problem, let's analyze the Venn diagram step-by-step using the given information:

1. Given Information:

   • $n(A \cup B) = 33$: This is the number of elements in the union of sets $A$ and $B$.
   • $n(A \cap B) = 8$: This is the number of elements in the intersection of sets $A$ and $B$.
   • $n(A) = 24$: This is the total number of elements in set $A$.
   • $n(A' \cup B) = 40$: This is the number of elements in the union of the complement of set $A$ and set $B$.

2. Determine Elements in Each Region:

   Let's denote the regions as follows for the Venn diagram with two sets $A$ and $B$:

   • Region X: Elements in $A$ only (i.e., $A - B$).
   • Region Y: Elements in both $A$ and $B$ (i.e., $A \cap B$).
   • Region Z: Elements in $B$ only (i.e., $B - A$).
   • Region W: Elements in neither $A$ nor $B$ (i.e., $A' \cap B'$).

3. Calculate Elements in Each Region:

   • Region Y (Intersection of $A$ and $B$): $n(Y) = n(A \cap B) = 8$

   • Region X (Only in $A$): $n(X) = n(A) - n(A \cap B) = 24 - 8 = 16$

   • Region Z (Only in $B$): To find $n(Z)$, we use the formula for the union: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ Solving for $n(B)$: $33 = 24 + n(B) - 8 \implies n(B) = 17$ Therefore, $n(Z)$ is: $n(Z) = n(B) - n(A \cap B) = 17 - 8 = 9$

   • Region W (Neither $A$ nor $B$): Using $n(A' \cup B)$: $n(A' \cup B) = n(U) - n(A \cap B')$ Let's find $n(A \cap B')$. We know that $A'$ is the complement of $A$, so we look at the number of elements outside of