# Venn Diagram Basics

The Oxford Dictionary defines the Venn diagram as “a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.” The venn diagram is a special case of the Euler diagram in that it shows all of the possible relationships between different sets. The Euler diagram shows only relevant relationships.

## Structure of Venn Diagrams

Venn diagrams, also known as set diagrams or logic diagrams, use overlapping circles to visually show the relationships between multiple sets of items. The circles are placed inside a rectangle that represents the universe, or universal set. Each circle in the rectangle represents all of the elements in a subset of the universal set. Everything outside a circle is the complement of that circle. For example, if a set is labeled A, everything outside the set A represents the complement of A. If a second set is labeled B, everything outside the set B represents the complement of B. The intersection of the subsets, or circles, represents all of the elements that are common to both subsets A and B.

For a Venn diagram with two circles, the universal set is identified as the intersection of the two subsets and their complements. The union of the two subsets A and B is denoted by A ∪ B. Likewise, the intersection of the two subsets A and B is denoted by A ∩ B.

## Purpose of Venn Diagrams

Venn diagrams offer a convenient way to visualize the logical relationships between different sets of items, or data. They are useful in set theory, the branch of mathematical logic that studies sets, but also offer a way to visualize real-life problems and are widely used in many fields. Because Venn diagrams offer a clear way to visualize the logical relationships among different groups or categories, they are popularly used in presentations, market analysis, or reports in any area where an analysis of the similarities or dissimilarities of groups is the focus, such as in the following examples:
• Venn diagrams are used in schools to teach basic math concepts as well as in higher education to teach advanced mathematics.