A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common. This type of diagram is used in scientific and engineering presentations, in theoretical mathematics, in computer applications, and in statistics. An element is a member of the intersection of two sets if and only if that element is a member of both sets. Venn diagrams are generally drawn within a large rectangle that denotes the universe , the set of all elements under consideration. In this example, points that belong to none of the sets X, Y, or Z are gray.
Points contained in all three sets are black.
Here is a practical example of how a Venn diagram can illustrate a situation. Let the universe be the set of all computers in the world. Let X represent the set of all notebook computers in the world. Let Y represent the set of all computers in the world that are connected to the Internet. Let Z represent the set of all computers in the world that have anti-virus software installed.