Venn Diagrams

Venn diagrams are a useful technique to demonstrate equivalence relationships in Boolean expressions. In a Venn diagram, the binary variables of a function are represented as overlapping areas in a Universe. Complementing or the NOT function is represented as the remainder of the Universe outside a given area. The Venn diagrammatic representations of , , and are illustrated below

Universe

In a Venn diagram the OR function is taken as the combination or union or areas while the AND function is the intersection or common part between two or more overlapping areas.

Two functions are said to be equivalent if they define identical areas on a Venn diagram.

For an example of the use of Venn diagrams see the Proof of de Morgan's Theorems by Venn diagrams in the Solved Problems at the end of this topic.