The problem is asking you to shade the region representing $B' \cup C$ on the Venn diagram.

Step-by-step solution:

1. Set $B'$: $B'$ represents the complement of set $B$, which means everything in the universal set $U$ except for the area inside circle $B$. So, you'll need to shade all areas outside circle $B$, including $C$ and any part of the universal set outside both circles.

2. Set $C$: The set $C$ includes everything inside circle $C$.

3. Union $B' \cup C$: The union $\cup$ means we combine all regions that are in either $B'$ or $C$. So, this means you will shade:

   • All of $C$, including its overlap with $B$.
   • All areas outside $B$, but inside the universal set $U$.

In summary, you will shade:

• The entire region of $C$ (the right circle).
• The region outside of $B$, including the area around both circles.

Would you like more details on any part of this solution? Here are some related questions for you:

1. How do we interpret $B'$ in relation to the universal set $U$?
2. What is the difference between union $\cup$ and intersection $\cap$?
3. How would you represent $B' \cap C$ on a Venn diagram?
4. What if the diagram had three sets instead of two? How would the union change?
5. Can you explain the difference between a universal set and a subset?

Tip: When solving Venn diagram problems, it's helpful to first identify the regions that are being excluded by any complements (e.g., $B'$).