The expression \((A \cup B \cup C)'\) represents the complement of the union of sets \(A\), \(B\), and \(C\). To break it down:

1. **Union**: The union \(A \cup B \cup C\) represents all elements that are in \(A\), \(B\), or \(C\) (or any combination of these sets).

2. **Complement**: The complement of the union \((A \cup B \cup C)'\) includes all elements that are **not** in the union. In other words, it consists of elements that do not belong to any of the sets \(A\), \(B\), or \(C\).

If you are working within a universal set \(U\), the result is:

\[
(A \cup B \cup C)' = U - (A \cup B \cup C)
\]

This is the set of all elements in the universal set that are not in \(A\), \(B\), or \(C\).

Would you like more details or examples on this? Here are some related questions:

1. What is the result of \((A \cup B)'\) in set theory?
2. How is the intersection of sets \((A \cap B)'\) handled?
3. What is the complement of the intersection \((A \cap B \cap C)'\)?
4. Can you explain De Morgan's laws for set operations?
5. How do you find the symmetric difference between two sets?

**Tip**: In set theory, the complement refers to elements outside the set, often within a defined universal set.

Explore the concept of the complement of the union of sets with the expression (A ∪ B ∪ C)'. This problem explains how to find elements not in sets A, B, or C using set theory principles. Learn about the union, complement, and application of De Morgan's laws. Suitable for students in Grades 9-12.

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