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!