To solve this, we can use set theory notation to find the values of the various set elements involving $C$ and $D$. We are given:

• The number of elements in the intersection of sets $C$ and $D$: $|C \cap D| = 8$
• The number of elements in the set difference $C \setminus D$: $|C \setminus D| = 6$

Let:

• $|C|$ be the total number of elements in set $C$.
• $|D|$ be the total number of elements in set $D$.
• $|C \cup D|$ be the total number of elements in the union of sets $C$ and $D$.

Since $|C \setminus D|$ represents the elements that are only in $C$ but not in $D$, we can express $|C|$ as: $|C| = |C \setminus D| + |C \cap D| = 6 + 8 = 14$

If you need to find any additional values, such as $|C \cup D|$, let me know, and I can guide you further!

Would you like more details on this solution?

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Here are five related questions that expand on this concept:

1. How can you calculate the union of two sets if you know their individual sizes and intersection?
2. What is the meaning of $|D \setminus C|$ in set theory?
3. How do you find the cardinality of sets when you have three overlapping sets?
4. Can you explain the principle of inclusion-exclusion with a practical example?
5. What would change in this calculation if $|D \setminus C|$ were given instead of $|C \setminus D|$?

Tip: When working with sets, always label known quantities carefully; this makes it easier to apply formulas for intersections and unions.