Let's analyze the problem step-by-step:

Given Information:

• $U = \{ f, g, h, p, q, r, x, y, z \}$
• $A = \{ g, h, q, r, z \}$
• $B = \{ q, r, x, y, z \}$
• $C = \{ h, p, q, y \}$

We are asked to find $C \cup (B \cap A')$, where:

• $A'$ is the complement of $A$ with respect to the universal set $U$.
• $B \cap A'$ is the intersection of set $B$ and the complement of set $A$.
• Finally, we find the union of set $C$ with $B \cap A'$.

Step 1: Find $A'$

The complement of $A$ (denoted $A'$) contains elements in $U$ but not in $A$: $A' = U \setminus A = \{ f, p, x, y \}$

Step 2: Find $B \cap A'$

The intersection of $B$ and $A'$ includes elements that are in both $B$ and $A'$: $B \cap A' = \{ x, y \}$

Step 3: Find $C \cup (B \cap A')$

Now, we find the union of $C$ and $B \cap A'$: $C \cup (B \cap A') = \{ h, p, q, y \} \cup \{ x, y \} = \{ h, p, q, x, y \}$

Conclusion:

The correct answer is $C \cup (B \cap A') = \{ h, p, q, x, y \}$.

If this was your attempt, you missed no elements, and the solution is correct. The answer provided in the input box matches the correct set.

Would you like any additional details or clarification? Here are five follow-up questions that might interest you:

1. What is the difference between the complement and the intersection of sets?
2. How do you calculate the union of two sets?
3. Can the complement of a set ever have elements that are also in the set itself?
4. What are some practical applications of set operations in computing or logic?
5. How does the size of the universal set affect set operations?

Tip: Always double-check which set operation you need to perform first—parentheses in set expressions work just like in algebra, defining the order of operations.