1. Thinking Mathematically Venn Diagrams and Set Operations

2. Venn Diagrams “Disjoint” sets have no elements in common. The set B is a “proper” subset of A. U BA U A B The sets A and B have some common elements. U A B

3. Definition of Intersection of Sets The intersection of sets A and B, written A  B, is the set of elements common to both set A and set B. This definition can be expressed in set builder notation as follows: A  B = { x | x  A AND x  B}

4. Definition of the Union of Sets The union of sets A and B, written A  B, is the set of elements that are members of set A or of set B or of both sets. This definition can be expressed in set-builder notation as follows: A  B = {x | x  A OR x  B}

5. The Empty Set in Intersection and Union For any set A: 1. A ∩  =  2. A   = A

6. De Morgan’s Laws (A U B)' = A' ∩ B': The complement of the union of two sets is the intersection of the complement of those sets. (A ∩ B)' = A' U B': The complement of the intersection of two sets is the union of the complement of those sets.