In the Venn diagram provided, we are asked to find the number of items in $T \cup W$, which represents the union of sets $T$ and $W$.

To find the total number of items in $T \cup W$, we sum the numbers in all regions that are part of either set $T$, $W$, or both. This includes:

• The 6 items in the left part of $T$ (not shared with $W$).
• The 5 items in the intersection (shared between $T$ and $W$).
• The 8 items in the right part of $W$ (not shared with $T$).

So, the total number of items in $T \cup W$ is:

$6 + 5 + 8 = 19$

Thus, there are 19 items in $T \cup W$.

Do you have any further questions, or would you like more details?

Related Questions:

1. What is the total number of items in the universal set $\xi$?
2. How many items are in $T \setminus W$ (only in set $T$)?
3. How many items are in $W \setminus T$ (only in set $W$)?
4. How many items are in the intersection of $T \cap W$?
5. What is the complement of $T \cup W$ in the universal set $\xi$?

Tip:

When solving union and intersection problems with Venn diagrams, carefully sum the distinct regions for unions, and focus on overlaps for intersections.