Venn Diagram

A Venn diagram is a way of illustrating sets. Here, a rectangle representing the universal set, usually denoted as U or E, is drawn. Inside the rectangle circles are typically drawn to represent sets. If the sets have elements in common, circles that represent sets must intersect. In the example, sets A and B are illustrated.

The universal set contains all of the elements in a given collection. For example, a universal set can be all positive integer numbers that are less than 10. Consider also two example sets A and B. U &={1,2,3,4,5,6,7,8,9} A &= { 1,2,3 } B &= { 3, 4, 5,6 } The above sets will now be illustrated with a Venn diagram. Since the number 3 belongs to both A and B it is placed in the overlapping region. Also, since the numbers 7, 8, and 9 are included in neither set, they are written outside the circles but inside the rectangle that represents the universal set.

In this example the circles have the same size even though the sets do not have the same number of elements. This means that Venn diagrams are generally not size proportional. For further exploration, Venn diagrams are useful to show relationships between sets like union, intersection, difference, and complement of sets.