To solve this problem, we need to determine the number of elements in each region of the Venn diagram. The regions correspond to the different parts of the sets $A$, $B$, and $C$, as well as the universal set $U$. We'll use the given cardinalities of the sets and their intersections to determine the number of elements in each of the eight regions.

Given Information:

• $n(U) = 44$ (total number of elements in the universal set)
• $n(A) = 18$ (number of elements in set $A$)
• $n(B) = 23$ (number of elements in set $B$)
• $n(C) = 26$ (number of elements in set $C$)
• $n(A \cap B) = 9$ (number of elements in the intersection of $A$ and $B$)
• $n(A \cap C) = 11$ (number of elements in the intersection of $A$ and $C$)
• $n(B \cap C) = 13$ (number of elements in the intersection of $B$ and $C$)

Let's denote each region of the Venn diagram as follows:

1. Region I: Elements in $A$ only.
2. Region II: Elements in $A \cap B$, but not in $C$.
3. Region III: Elements in $A \cap C$, but not in $B$.
4. Region IV: Elements in $A \cap B \cap C$ (all three sets).
5. Region V: Elements in $B$ only.
6. Region VI: Elements in $B \cap C$, but not in $A$.
7. Region VII: Elements in $C$ only.
8. Region VIII: Elements outside all three sets, but in $U$.

Step-by-Step Solution:

1. Region IV ($A \cap B \cap C$):

   • This is the number of elements common to all three sets, and it is included in all the intersections.
   • Let's denote this as $x$.
   • We will calculate it last after checking the individual and two-set intersections.

2. Region II ($A \cap B$, but not in $C$):

   • The total number of elements in $A \cap B$ is 9.
   • Out of these, some elements are also in $C$. So, subtract the elements in $A \cap B \cap C$ (denoted as $x$).
   • Region II = $9 - x$.

3. Region III ($A \cap C$, but not in $B$):

   • The total number of elements in $A \cap C$ is 11.
   • Subtract the elements in $A \cap B \cap C$ (denoted as $x$).
   • Region III = $11 - x$.

4. Region VI ($B \cap C$, but not in $A$):

   • The total number of elements in $B \cap C$ is 13.
   • Subtract the elements in $A \cap B \cap C$ (denoted as $x$).
   • Region VI = $13 - x$.

5. Region I ($A$ only):

   • The total number of elements in $A$ is 18.
   • Subtract the elements that are also in $B$, $C$, and $A \cap B \cap C$.
   • Region I = $18 - ((9 - x) + (11 - x) + x)$.

6. Region V ($B$ only):

   • The total number of elements in $B$ is 23.
   • Subtract the elements that are also in $A$, $C$, and $A \cap B \cap C$.
   • Region V = $23 - ((9 - x) + (13 - x) + x)$.

7. Region VII ($C$ only):

   • The total number of elements in $C$ is 26.
   • Subtract the elements that are also in $A$, $B$, and $A \cap B \cap C$.
   • Region VII = $26 - ((11 - x) + (13 - x) + x)$.

8. Region VIII (Outside all three sets):

   • The total number of elements in $U$ is 44.
   • Subtract the elements in $A$, $B$, and $C$ (all regions of the Venn diagram).
   • Region VIII = $44 - (Region I + Region II + Region III + Region IV + Region V + Region VI + Region VII)$.

Once you solve for $x$, substitute it back into the equations for the other regions. Would you like me to proceed with calculating $x$ and the other regions?