Unions and Intersections

The union of two sets A and B, written A U B, is the set of elements which are either in set A, set B, or both. The intersection of two sets A and B, written A B, is the set of elements which are in both A and B. If figures have nothing in common, then their intersection is the null or empty set, written Ø or { }.

Perhaps the best way to present these is the Venn diagram. The Venn diagram, invented by John Venn (1834 - 1923) in the late 19th century, is a simple kind of organizational picture. A rectangle represents the universe (the set of all elements). Circles inside the rectangle represent any sets you need. Circles can cross to show intersection, and can have inner circles to represent subsets.

As you can see in the diagrams, to show intersection you darken the area shared by the two sets. To show the union of the two sets, you darken both of them. In the first picture, the sets are disjointed because they have no elements in common. A B means that A is an element or subset in B.

- Jaime III
"Definition of fraud - knowingly selling bad chips as good for five months." - Anonymous