Venn Diagram – Definition

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Venn Diagram Definition

A Venn diagram refers to an illustration that makes use of circles, be it overlapping or non-overlapping, in order to portray a relationship between finite sets of things. Venn diagram was named after John Venn in 1880. He was an English professor, as well as, logician.

A Little More on What is a Venn Diagram

Typically, the Venn diagram’s basic structure is the overlapping circles, where items present in the overlapping section bear a commonality. Items that reside in the outer parts of the circles don’t share common traits that are specified.

Venn diagrams have long been known for their educational usefulness. Since the middle of the 20th century, these diagrams have been utilized as an aspect of the introductory logic curriculum and also in basic-level educational plans all over the world.

John Venn, the English logician, invented this diagram in 1880. But, he originally referred to the illustration as Eulerian circles. The term, Venn didn’t surface until 1918 when a United States academic professor and also the eventual originator of conceptual pragmatism, Clarence Lewis, called the circular illustration as the Venn diagram in his book titled “A Survey of Symbolic Logic.”

At Cambridge University, Venn studied and also taught logic and probability theory. He developed his method of using Venn diagrams to depict set theory. He published a prolific and precedent-setting work titled “The Logic of Chance”, a book which explained the frequency theory of probability. He opined that probability should be established based on the regularity of the prediction of something occurring, as against popular educated assumptions. Venn was also able to develop and more fully realize the theories of the mathematician, George Boole in his book titled “Symbolic Logic” in 1881. In this work, Venn highlighted what eventually became known as Venn diagram.

While Venn diagrams are, at an elementary level, easy pictorial depictions of the relationship existing between two sets of things, their orientation, as well as, applications are much more complex. Still, the Venn diagram’s streamlined purpose has brought about their popularized use to depict concepts and groups. Furthermore, they are seen as trademark tools for the teaching of beginners’ logic and math.

Example of a Venn Diagram

Try drawing a Venn diagram to analyze four-legged animals, as well as, domesticated ones. Obviously, a large number of animals have four legs. On the contrary, how many of these four-legged animals have been domesticated? Two examples of four-legged animals that will reside in the overlapping space of the two circles are dogs and cats. A tiger, however, will fall only in the circle depicting four-legged animals while a chicken will be an instance of a domesticated animal which doesn’t have four legs and thus will belong only in the circle depicting domesticated animals.

References for Venn Diagram

Academic Research on Venn diagram

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R, Chen, H., & Boutros, P. C. (2011). BMC bioinformatics, 12(1), 35.

A survey of Venn diagrams, Ruskey, F., & Weston, M. (1997). Electronic Journal of Combinatorics, 4, 3.

venn: an interactive Venn diagram viewer, Bardou, P., Mariette, J., Escudié, F., Djemiel, C., & Klopp, C. (2014). BMC bioinformatics, 15(1), 293.

Venn diagrams and independent families of sets, Grünbaum, B. (1975). Venn diagrams and independent families of sets. Mathematics Magazine, 48(1), 12-23.

InteractiVenn: a web-based tool for the analysis of sets through Venn diagrams, Heberle, H., Meirelles, G. V., da Silva, F. R., Telles, G. P., & Minghim, R. (2015). BMC bioinformatics, 16(1), 169.

Generalized Venn diagrams: a new method of visualizing complex genetic set relations, Kestler, H. A., Müller, A., Gress, T. M., & Buchholz, M. (2004). Bioinformatics, 21(8), 1592-1595.

Interactive textbook and interactive Venn diagram: natural and intuitive interfaces on augmented desk system, Koike, H., Sato, Y., Kobayashi, Y., Tobita, H., & Kobayashi, M. (2000, April). In Proceedings of the SIGCHI conference on Human Factors in Computing Systems (pp. 121-128). ACM.

VENNFS: A Venndiagram file manager, De Chiara, R., Erra, U., & Scarano, V. (2003, July). Proceedings. Seventh International Conference on (pp. 120-125). IEEE.

Exact and approximate area-proportional circular Venn and Euler diagrams, Wilkinson, L. (2012). IEEE transactions on visualization and computer graphics, 18(2), 321-331.

On the construction of venn diagrams1, More, T. (1959). The Journal of Symbolic Logic, 24(4), 303-304.

The construction of Venn diagrams, Grünbaum, B. (1984). The Two-Year College Mathematics Journal, 15(3), 238-247.

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