https://file.aiquickdraw.com/mathbot/file/17264275701858i9ped9c.jpg

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.

How many items are in T ∪ W based on the provided Venn diagram?

Learn how to find the number of items in the union of sets T and W using the Venn diagram provided. Understand key concepts from set theory, including the principle of inclusion-exclusion, with a step-by-step solution. Suitable for students in Grades 6-8.

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