There are 12 students who attend both classes and 2 students who do not take either of the subjects. Example 1: Subjects Taken by StudentsĪ study is being done at a school on students who take the subjects mathematics and economics. Below are examples of uses of Venn diagrams. Using Venn DiagramsĪs highlighted above, Venn diagrams are used in several ways to show relationships between various set elements.
Venn diagrams were adopted in various disciplines and complexities aided by evolving technology and the use of computers. The term Venn diagram was first published by Clarence Irvine Lewis in his 1918 book, “A Survey of Symbolic Logic.” Mathematicians and logicians continued to improve the diagrams in the 19 th and 20 th centuries to show clearer and more complex relationships using more sets.
John Venn referenced Euler in his diagrams, which he first described as Euler circles. He drew what he defined as Euler diagrams. There are various other logicians who also drew similar diagrams, but the closest diagrams that resemble Venn diagrams were first drawn by Leonard Euler in the 1700s. It was first published in his 1980 journal titled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.” However, the development of Venn diagrams can be traced back to the 1200s through philosopher and logician Ramon Llull, who drew similar types of diagrams. The Venn diagram concept was established by British mathematician and logician John Venn. The diagram below shows the absolute complement of X in U – i.e., everything in the universe except for X (grey area). An equation to illustrate the complement of X is X C = U/A, where U represents a given universe of elements. Intersection represents shared elements (in the middle) within sets X and Y.Ĭomplement (X C): Represents whatever is not represented in a particular set in this case, everything not in set X. Intersection (∩): Represents all elements shared or common within the selected sets or groupings. Union (∪): Represents the union of all sets – i.e., the universe of all elements within X and Y sets. They are related to Euler diagrams, which only differ in that they do not illustrate a set if there are no elements present. Venn diagrams provide a powerful visual display of data, commonly used in presentations and business and scientific reports. An example of a Venn diagram above shows three sets labeled X, Y, and Z and the corresponding relationships between elements in each set. They are mainly used in set theory and also to illustrate relationships between elements in various areas, such as statistics, logic, probability, linguistics, business, and computer science. It aims to provide a graphical visualization of elements, highlighting the similarities and differences between them. It is also referred to as a set diagram or logic diagram.Ī Venn diagram uses multiple overlapping shapes (usually circles) representing sets of various elements. It is a diagram that shows all the possible logical relationships between a finite assemblage of sets or groups. A Venn diagram is a schematic representation of the elements in a set or a group.
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