Abstract
The essay will mainly deal with different aspects of mathematical tools, the definition and its inventor, various uses of the Venn diagram and its importance. It will also focus on the usage of the Venn diagram as a tool for mathematical and analytical problems. The paper will appreciate the different sets of the Venn diagram demonstrating how it appears and their different purposes.
Introduction
Venn Diagrams is a presentation that shows the mathematical and the logical set up of series of events pictorially in the form of circles and closed curves. The circle and the curves are enclosed in a rectangular drawing with the inclusion of universal sets and simple basic of groups and sets. The regions in the rectangle are represented by regions of overlapping within the circles. The Venn diagram was invented in 1880 by John Venn. The main focus of the essay will be the primary uses of the Venn diagram highlighting its importance in assisting the students to solve various mathematical problems. Other names for the Venn diagram include set diagram, logic diagram and primary diagram. The essay will also cover the different types of the Venn diagram.
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Sets of the Venn diagrams
There are different presentations of the Venn diagram with each pointing out how it is related to the sets that are under study. Different sets of the Venn diagram also depict how they are used in the solution of the problems at hand. One type of the Venn diagram is the disjoint set. The characteristics of the disjoint set include the fact that it has none of its peripheral sides overlapping with the other, and it also has an empty intersection (Conway, 2010). The Van diagram is drawn with no intersection if it is used in a situation of two sets with no commonality.
Venn diagrams vary depending on the presentation of the elements that are to be used. They include the two-set Venn diagram, three-set Venn diagram, four-set Venn diagram, five-set Venn diagram and the multiple Venn diagram. The two-set Venn diagram is the most basic form. The two circles appear as if they are intersecting or overlapping but they do not in real sense. What is seen is the two-set Euler diagram (Chen & Boutros, 2011). When one set is fully enclosed in another, it is referred as being both Euler and a Venn diagram.
The three set Venn diagram has three circles of overlapping and intersecting with each other. After intersection, they form seven sections in the entire diagram with a common point known as the center. The center forms the union of the three sets as asserted by Conway (2010). The four set Euler diagram has got four different sets ramping up together. Here, the circles are no longer used like in the other cases because it would be difficult to notice the center point. Therefore, the oval shapes are essential in making sure that all the four required sets are included in the Venn diagram.
The five-set Venn diagram also requires the use of oval shapes so as to determine the center of the diagram. Finally, the multi-set Venn diagram, just as the name suggests, includes the use of various sets preferably more than five to make a presentation of the elements under study.
Importance of the Venn diagram
The Venn diagram is a vital tool in helping mathematicians in comparing and contrasting various objects, people, scenarios and events through simple brainstorming. To use the Venn diagram to make comparisons, one has to consider the need to use the same diagram for the purposes of classifying the objects. According to Martin et al ., (2012), the drawn diagrams should always meet the needs of the user, and they don't have to intersect or overlap or to be of equal sizes. The user must be very keen while dealing with the diagrams to solve problems. First, one has to draw and label the universal set and also be able to use more complex diagrams that will assist them to learn new ways to think and organize the different elements of the study (Shade & Handelsman, 2012).
The Venn diagram has played a critical role in making the work of the students easier. One example of this is its ability to be used in proverbial terms. They say that a picture is worth a thousand words and in reality; the Venn diagram has assisted many students in the easy reading of the data helping them analyze it. The Venn diagram is easier to read and interpret than the statement form of the data sets (Martin et al ., 2012). From the pictorial analysis of the Venn diagram, one can write a comprehensive essay that can be used to explain series of events that have taken place without necessarily going to the primary source of information.
In conclusion, it is vital to note the importance of the Venn diagram as a tool of analysis and interpretation of data and the way it has assisted many students in the course of their study. It is therefore very important to be well acquainted in drawing and interpreting it.
References
Chen, H., & Boutros, P. C. (2011).Venn Diagram: a package for the generation of highly-customizable Venn and Euler diagrams in R. BMC Bioinformatics , 12 (1), 35.
Conway, D. (2010). The data science Venn diagram. Drew Conway , 10 .
Martin, B., Chadwick, W., Yi, T., Park, S. S., Lu, D., Ni, B., ...&Maudsley, S. (2012). VENNTURE–a novel Venn diagram investigational tool for multiple pharmacological dataset analysis. PLoS One , 7 (5), e36911.
Shade, A., &Handelsman, J. (2012).Beyond the Venn diagram: the hunt for a core microbiome. Environmental Microbiology , 14 (1), 4-12.
