Title: 2MEN_ 03_INF_EN_01**

Commutative Laws

Unbenannter Text

- Union: \( A \cup B = B \cup A \)
- Intersection: \( A \cap B = B \cap A \)

These laws state that the order in which you take the union or intersection of two sets doesn't matter.

Associative Laws

Unbenannter Text

- Union: \( (A \cup B) \cup C = A \cup (B \cup C) \)
- Intersection: \( (A \cap B) \cap C = A \cap (B \cap C) \)

These laws indicate that when taking the union or intersection of multiple sets, the grouping of the sets doesn't affect the result.

Distributive Laws

Unbenannter Text

- Intersection distributes over Union: \( A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \)
- Union distributes over Intersection: \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \)

These laws describe how union and intersection distribute over each other.

Identity Laws

Unbenannter Text

- Union with the empty set: \( A \cup \emptyset = A \)
- Intersection with the universal set: \( A \cap U = A \)

These laws state that the union of any set with the empty set is the set itself, and the intersection of any set with the universal set (the set containing all possible elements) is the set itself.

Domination Laws

Unbenannter Text

- Union with the universal set: \( A \cup U = U \)
- Intersection with the empty set: \( A \cap \emptyset = \emptyset \)

These laws state that the union of any set with the universal set is the universal set, and the intersection of any set with the empty set is the empty set.

Idempotent Laws

Unbenannter Text

- Union: \( A \cup A = A \)
- Intersection: \( A \cap A = A \)

 These laws indicate that the union or intersection of a set with itself is the set itself.

Complement Laws

Unbenannter Text

- Union with complement: \( A \cup A' = U \)
- Intersection with complement: \( A \cap A' = \emptyset \)
- Double complement: \( (A')' = A \)

These laws describe the relationship between a set and its complement (everything not in the set).

Absorption Laws

Unbenannter Text

- Union: \( A \cup (A \cap B) = A \)
- Intersection: \( A \cap (A \cup B) = A \)

These laws state that combining a set with the intersection or union of itself and another set will give you the original set.

De Morgan's Laws

Unbenannter Text

- Complement of Union: \( (A \cup B)' = A' \cap B' \)
- Complement of Intersection: \( (A \cap B)' = A' \cup B' \)

These laws describe how the complement of a union or intersection can be expressed as the intersection or union of the complements, respectively.