The expression $(A \cup B)' \cap C$ represents a set-theoretic operation involving the union, complement, and intersection of sets. Here's a breakdown of how to evaluate this:

1. $A \cup B$: This is the union of sets $A$ and $B$, which includes all elements that are in either $A$, $B$, or both.

2. $(A \cup B)'$: This represents the complement of $A \cup B$, which includes all elements not in the union of $A$ and $B$. In other words, it contains elements that are outside both $A$ and $B$.

3. $(A \cup B)' \cap C$: Now, this is the intersection of $(A \cup B)'$ with $C$. This means we're looking for all elements that are in $C$, but also not in $A \cup B$.

Interpretation:

• You're finding elements that belong to set $C$ but do not belong to either set $A$ or set $B$.

If you have specific sets for $A$, $B$, and $C$, you can directly compute the resulting set.

Would you like a detailed example with specific sets or further clarification?

---

Relative Questions:

1. How is the union of sets $A$ and $B$ different from their intersection?
2. What is the difference between a complement and an intersection in set theory?
3. Can you give an example where $A \cup B = A \cap B$?
4. What are De Morgan's laws in set theory, and how do they apply here?
5. How would the operation change if we used $A \cap B$ instead of $A \cup B$?

Tip: Always use Venn diagrams when working with set operations to visually interpret the relationships!