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To solve for \((A \cup B \cup C)'\), we need to determine the complement of the union of sets \(A\), \(B\), and \(C\), which means finding the elements that are not in any of these sets.

### Step-by-step approach:
1. **Union of Sets (\(A \cup B \cup C\))**: This includes all the elements that belong to at least one of the sets \(A\), \(B\), or \(C\).
   - **Set A**: Making flowers, Nephew, Cat
   - **Set B**: Spiderman, Sports
   - **Set C**: Crafting, Fall, Camping
   - **Common Elements**: 
     - **Set A and B Intersection**: Pets
     - **Set A and C Intersection**: None.
     - **Set B and C Intersection**: None.
     - **Set A, B, C Intersection**: Teaching, Family

   Thus, \(A \cup B \cup C\) includes:
   - Making flowers, Nephew, Cat (from A)
   - Spiderman, Sports (from B)
   - Crafting, Fall, Camping (from C)
   - Pets, Teaching, Family (from intersections)

   The union of all sets includes these elements: 
   \[
   A \cup B \cup C = \{\text{Making flowers, Nephew, Cat, Spiderman, Sports, Crafting, Fall, Camping, Pets, Teaching, Family}\}
   \]

2. **Complement of the Union**:
   The complement is everything **outside** of this union. Based on the diagram, there are no additional elements outside of the listed sets, so the complement \((A \cup B \cup C)'\) would be the empty set \(\emptyset\) — meaning there are no elements outside the union of the sets.

Thus, \((A \cup B \cup C)' = \emptyset\).

Would you like further explanation or details on any specific part?

Here are five related questions:
1. What is the union of just \(A\) and \(B\)?
2. How do we find the intersection of sets \(A\) and \(C\)?
3. What is the complement of \(A\) alone?
4. What would \(A' \cup B'\) represent in this case?
5. Can a set's complement ever be larger than the set itself?

**Tip:** The complement of a set depends on the universal set being considered. Always define your universal set when working with complements!

Learn how to find the complement of the union of sets A, B, and C. This problem covers set theory concepts like union and complement, with a detailed step-by-step solution. Suitable for students in Grades 6-8.

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