To illustrate the expression $(A \cup B') \cap C$ using a Venn diagram, we need to understand the components involved in the expression:

1. $A$: A set represented by a circle.
2. $B'$: The complement of set $B$, which includes everything outside of set $B$.
3. $C$: Another set represented by a circle.

The expression $(A \cup B') \cap C$ involves two main operations:

• Union ($A \cup B'$): Includes all elements that are in either set $A$ or set $B'$ (i.e., not in $B$).
• Intersection with $C$ ($\cap C$): Only includes elements that are also in set $C$.

Here's how you can draw the Venn diagram step-by-step:

1. Draw three overlapping circles:

   • Label the first circle as $A$.
   • Label the second circle as $B$.
   • Label the third circle as $C$.

2. Shade $A \cup B'$:

   • Shade the area within circle $A$.
   • Shade the area that is outside circle $B$ (this represents $B'$).

3. Find the intersection with $C$:

   • Identify the region that is both shaded from the previous step ($A \cup B'$) and also inside circle $C$.
   • Shade this overlapping region within $C$.

This final shaded region in circle $C$ represents $(A \cup B') \cap C$. The key is recognizing that $A \cup B'$ is all of $A$ and everywhere outside $B$, and then intersecting that with $C$ focuses on where these shaded areas overlap $C$.

If drawn properly, you will have a correctly visualized Venn diagram for the expression $(A \cup B') \cap C$.