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The image contains a mathematical statement invoking **De Morgan's Law** for sets. It states the following:

Given a collection of sets \( F_a \) indexed by \( a \in I \), the complement of the intersection of these sets is equal to the union of the complements of the individual sets:

\[
F^c = \left( \bigcap_{a \in I} F_a \right)^c = \bigcup_{a \in I} F_a^c
\]

This is a direct application of **De Morgan's Laws** for sets:

1. The complement of an intersection of sets is the union of the complements:
   \[
   \left( \bigcap_{a \in I} F_a \right)^c = \bigcup_{a \in I} F_a^c
   \]

2. Similarly, the complement of a union of sets is the intersection of the complements:
   \[
   \left( \bigcup_{a \in I} F_a \right)^c = \bigcap_{a \in I} F_a^c
   \]

These laws are fundamental in set theory and are widely used in proofs and logical manipulations.

Do you have any further questions or would you like a deeper explanation? 

Here are some related questions you might find useful:
1. How can De Morgan’s Law be applied in probability theory?
2. What is the significance of complements in set theory?
3. How does De Morgan's Law extend to logical statements?
4. What are some common uses of set complements in real-world applications?
5. Can you provide an example that illustrates De Morgan’s Laws with real sets?

**Tip**: De Morgan's Laws are extremely useful when dealing with complex logical statements or sets, as they allow you to simplify expressions involving intersections and unions.

The user provided an image showing a mathematical statement applying De Morgan's Law to sets, focusing on the complement of intersections and unions.

Learn how De Morgan's Law applies to set theory with a focus on the complement of intersections and unions. This problem demonstrates how to manipulate sets using De Morgan’s theorem, useful for students studying advanced set theory concepts.

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