The expression \( A^c \cap B^c \) represents the intersection of the complements of sets \( A \) and \( B \). 

This can be understood through **De Morgan's Laws** in set theory, which state:

\[
A^c \cap B^c = (A \cup B)^c
\]

### Explanation:
- \( A^c \) is the complement of set \( A \), meaning it includes all elements not in \( A \).
- \( B^c \) is the complement of set \( B \), meaning it includes all elements not in \( B \).
- \( A^c \cap B^c \) is the set of elements that are not in \( A \) and also not in \( B \). This is equivalent to the complement of the union of \( A \) and \( B \).

### Summary:
\[
A^c \cap B^c = (A \cup B)^c
\]

This is a key result in set theory and is useful in various applications, including probability and logic.

Would you like further details or have any questions?

### Relative Questions:
1. What are the implications of De Morgan's Laws in probability?
2. How can \( A^c \cap B^c \) be visualized using a Venn diagram?
3. How does the intersection of complements relate to logical AND and OR operations?
4. Can you provide an example with specific sets for \( A \) and \( B \)?
5. What is the difference between \( A^c \cap B \) and \( A \cap B^c \)?

**Tip:** Understanding set operations and their complements is crucial in probability, logic, and various branches of mathematics.

Explore the intersection of complements in set theory with the expression A^c ∩ B^c. Learn about De Morgan's Laws and their application in set operations. This concept is crucial in probability, logic, and various mathematical applications. Suitable for advanced high school students and beyond.

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