To solve this Venn diagram problem, we are asked to shade the region that represents $C \cup (A' \cap B')$. Let's break down the expression and shade accordingly:

1. Complement of $A$ ($A'$): This is everything outside of set $A$.
2. Complement of $B$ ($B'$): This is everything outside of set $B$.
3. Intersection of $A'$ and $B'$ ($A' \cap B'$): This is the region that lies outside both $A$ and $B$, meaning the area that is outside both of these sets.
4. Union with $C$ ($C \cup (A' \cap B')$): This means we will take the area of set $C$ and combine it with the region we found in step 3 (outside both $A$ and $B$).

Steps to Shade the Diagram:

• First, shade all of set $C$.
• Then, shade the region that is outside both $A$ and $B$ (the part outside both circles $A$ and $B$).
• The result will be a combination of both areas.

Would you like more details on any of these steps?

Related Questions:

1. What does the intersection of three sets $A \cap B \cap C$ look like on a Venn diagram?
2. How would you represent the union of three sets $A \cup B \cup C$?
3. What does $A \cap B'$ represent, and how would it be shaded?
4. How does the universal set $U$ affect Venn diagram calculations?
5. Can you explain the difference between $A'$ and $A \cap B$?

Tip: When working with complements in Venn diagrams, always start by identifying which regions do not belong to the sets in question. This makes it easier to visualize the desired regions.