To solve $r(A \cup C')$ using the roster method, we first need to define the sets $A$, $C$, and the universal set $U$ (from which we'll take the complement $C'$).

General Procedure:

1. List the elements of set $A$ in roster form: The elements of $A$.
2. List the elements of set $C$ in roster form: The elements of $C$.
3. Find the complement of $C$ (i.e., $C'$): This includes all elements in the universal set $U$ that are not in $C$.
4. Perform the union $A \cup C'$: This gives all elements that are in $A$ or $C'$, or both.
5. List the result in roster form.

If you provide the specific elements of sets $A$, $C$, and the universal set $U$, I can give you the exact solution.

Would you like to clarify the sets or