The image contains a set of questions related to Venn diagrams and set theory. It asks for Venn diagrams to be shown for the following set operations:

1. $P - (Q \cap R)$
2. $(P \cup Q) \cap R$
3. $P - Q$
4. $(A \cup B)^C$
5. $A^C \cap B^C$
6. $A^C \cup B^C$

I will now explain each operation and how you could draw the corresponding Venn diagrams.

Explanation:

1. $P - (Q \cap R)$: This represents the set of elements in $P$ but not in the intersection of $Q$ and $R$.

2. $(P \cup Q) \cap R$: This represents the set of elements that are in both $R$ and in either $P$ or $Q$.

3. $P - Q$: This represents the set of elements in $P$ but not in $Q$.

4. $(A \cup B)^C$: This represents the complement of the union of sets $A$ and $B$, meaning the set of elements that are in neither $A$ nor $B$.

5. $A^C \cap B^C$: This is the intersection of the complements of $A$ and $B$, which also represents the elements that are neither in $A$ nor in $B$ (equivalent to $(A \cup B)^C$).

6. $A^C \cup B^C$: This is the union of the complements of $A$ and $B$, meaning elements that are either not in $A$ or not in $B$.

Would you like me to draw the corresponding Venn diagrams or provide additional details on each operation?

Here are some relative questions to expand on this topic:

1. How does the complement operation change the areas shaded in a Venn diagram?
2. Can you explain the relationship between the union and intersection of sets visually?
3. What is the difference between the intersection and difference of two sets?
4. How does De Morgan’s Law apply to the complements of unions and intersections?
5. How would these diagrams change if we added a universal set?

Tip: Understanding the basic set operations (union, intersection, difference, and complement) is crucial for mastering set theory and Venn diagrams.