Finite Mathematics

Robert S. Wilson

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