To find $A \cup C'$ using the roster method, follow these steps:

1. Understand the Sets:

• $A$ is a set of elements.
• $C'$ (C prime) refers to the complement of set $C$, meaning all elements not in $C$ but within the universal set $U$.

2. Define the Universal Set (U):

We need a universal set $U$, which includes all elements being considered for the problem. This is crucial because $C'$ is defined with respect to $U$.

3. Identify $A$ and $C$:

• Use the given sets of $A$ and $C$ to determine their elements.

4. Complement $C'$:

• List all elements from the universal set $U$ that are not in $C$.

5. Find $A \cup C'$:

• The union $A \cup C'$ is the set of all elements that are in either $A$, $C'$, or both. No repetitions are allowed.

If you provide the sets $A$, $C$, and the universal set $U$, I can help you calculate $A \cup C'$ specifically.

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Would you like to provide the sets, or should I proceed with an example?

Follow-up questions:

1. What is the universal set for your problem?
2. What is the set $A$?
3. What is the set $C$?
4. Would you like help finding the complement of $C$ first?
5. Would you like me to show an example with arbitrary sets?

Tip: The union of two sets contains all distinct elements from both sets combined, with no duplicates.