An Introduction to Set Theory

Everyone knows the relational model is founded on logic and set theory, and moreover that it derives much of its strength, rigor, and robustness from those solid foundations. Few database professionals can claim to be familiar with logic or set theory, however, even though an elementary knowledge of those disciplines is critical to successful use of a relational DBMS. This presentation is offered to help rectify the situation. It explains the basic concepts of set theory, showing both (a) their relationship to predicate logic and (b) their direct applicability to a variety of database issues.

The presentation is divided into three modules. Module I covers sets and their properties, set inclusion, and power sets. Module II covers union, intersection, difference, complement, and exclusive union (symmetric difference). Module III covers certain important identities, the algebra of sets, ordered pairs, cartesian product, and relations.