## 2. Set Operations

**Theorem 2.1:
(Commutativity of Unions) Let A and B be two sets. then**

**Theorem 2.2**:
**(Commutativity of Intersections)** Let A and B be two sets. then

**Theorem 2.3**:
**(Associativity of Unions)** Let A, B, and C be three sets. then

**Theorem 2.4**:
**(Associativity of Intersections)** Let A, B, and C be three
sets. then

**Theorem 2.5**:
**(Distributivity of Intersections across Unions)** Let A, B, and
C be three sets. then

.
**Theorem 2.6**:
**(Distributivity of Unions across Intersections)** Let A, B, and
C be three sets. then

**Theorem 2.7**:
**(Transitivity of Inclusion)** Let A, B, and C be three sets. If

then

**Theorem 2.8**:
**(The Distributivity of Cartesian Products Across Unions)**. Let
A, B, and C be three sets. If

**Theorem 2.9**:
**(The Distributivity of Cartesian Products Across
Intersections)**. Let A, B, and C be three sets. If

**Theorem 2.10**:
Let A and B be two sets. Then

**Theorem
2.11**: Let A and B be two sets. Then

3. Functions