Applications for Venn Diagrams

A Venn diagram depicts how groups interact with one another, with groups referred to as “sets.” Venn diagrams are often made up of two to three circles (or other forms) that overlap, however depending on the number of sets, a diagram can have more shapes.

Every form represents a group of numbers, objects, or ideas. When two sets of values have comparable values, they appear as overlapping areas known as “intersections.”

Venn diagrams are named after John Venn, an English logician. Venn diagrams, like Euler diagrams, are supposed to represent all conceivable relationships between two or more groups being investigated, even if one or more of the sets has no values.

How do you draw a Venn diagram?

Following these steps will help you construct a Venn diagram

1. Define your analysis parameters

First, decide what you want to achieve, such as making a critical decision or comprehending hard issues. Determine how many thoughts, ideas, numbers, or objects will be involved next. Then, decide on the type of Venn diagram you want to create by deciding how you want to depict each set’s relationship to one another.

2. Make your own universe

Create an area or “universe” in which all the other shapes will sit once you’ve decided what you want to do with your Venn diagram. This is usually a rectangle. To uncover possible linkages among the sets, make sure the other forms overlap.

3. Clearly label all of your settings

Set names should reflect simple or simplified concepts that apply to all of the data in each set. If you were comparing two characters from a story, you would label the sets with the characters’ names. In mathematics, sets are frequently labelled with single letterforms (such as A, B, C, and so on).

4. Fill up the Venn diagram with data

Place all data on the diagram according to its set if you want to study it all. If data from one set intersects with data from another, write the information just once, at the intersection.

5. Examine the information

Examine each set for similar information, consider the differences, and develop your findings. If you’re trying to make a big decision, the disparities you find across groups will help you reach a decision.

What three sorts of Venn diagrams are there?

Venn diagrams aid in the expression of ideas and the analysis of facts. The three primary types are as follows:

Diagrams by Venn

Venn started with two symmetrical closed curves (circles) while creating his diagram, however he allowed for diagrams with three or more shapes:

• Diagram with two circles. The two-circle Venn diagram depicts the relationship between two sets of data. The two circles are normally vertically overlapping, with one on the left and the other on the right.

• Diagram with three circles. His three-circle graphic depicts the link between three different types of data. Two of the sets are usually positioned as if there were just two sets of information accessible, while the third intersects the other two horizontally (up or down).

• Diagram with four circles. For intersections of all forms to be conceivable, his four-shaped diagram will lose symmetry. Venn devised a four-shape diagram consisting of three circles and a curved shape. He may have also made a diagram with four ellipses.

Venn created sets with more than four curves that interweaved with earlier curves while intersecting with the original three sets.

Diagram by Branko Grünbaum

Mathematician Branko Grünbaum drew a Venn diagram using five sets:

• Congruent, rotationally symmetrical ellipses appear in the diagram.

• At a huge junction, all shapes come together.

• There are 25 smaller crossroads.

A Branko Grünbaum Venn diagram contains 31 sections in total. Some mathematicians play around with it, placing integers in all five sets (A, B, C, D, and E) so that the sum in each is the same.

Venn diagrams by Edwards

Anthony William Fairbank Edwards, a British statistician, devised a series of diagrams that accounted for three or more sets:

• Diagram with three sets. Two rectangles intersect a circle at right angles in his three-set diagram (one rectangle is oriented horizontally and the other vertically).

• Diagram with four sets. His four-set diagram features a shape that resembles a tennis ball seam and rests around the circle’s centre. The seam shape’s length stretches vertically.

• Four sets plus a diagram. Beyond the first four sets, Edwards allowed for cogwheel forms with double the number of teeth as the preceding one. Each of these shapes is centred on the universe’s core.

Applications for Venn Diagrams

Venn diagrams are commonly seen in mathematical situations, but they are also used by businesses and professionals. In each situation, the individual generating the image is attempting to solve a problem, make a critical decision, forecast probability, or comprehend or depict the relationships between different sets, concepts, or things. A Venn diagram can be beneficial in the following situations:

Mathematics

Mathematical Venn diagrams enable scholars to address difficult problems such as:

• Union problem

A union problem requires students to place all of the numbers in all of the sets on the diagram.

• Intersection problem

Students are instructed to place just the numbers that overlap on the diagram in an intersection issue. If the problem specifies three numbers (1, 15, and 27) and seven numbers (1, 3, 14, 19, 21, 25, and 27), only 1 and 27 will appear on the diagram at the intersection of the circles.

• Symmetric problem 

A symmetric difference of two sets necessitates the representation of only the numbers that do not overlap in the image.

• Absolute problem 

An absolute complement of one set necessitates the representation on the diagram of all the numbers that are not in that set.

Business

Venn diagrams are used in a variety of corporate settings, particularly in slideshow presentations. Other options include:

• Market analysis: overlapping areas comprise the company’ target market when two or more sets of information are used.

• Competitor analysis: A company can only compare itself to competitors using two sets of data to evaluate how they differ or are similar. This aids in the discovery of benefits and the emphasis of improvements.

• Product comparison: As seen in the overlapping sections, an image with overlapping forms can help assess the benefits of two or more product concepts to identify which elements of a product are the most desirable.

• Decision-making: The same rules that apply to examining two or more product ideas also apply to the broader decision-making process of a firm.

Other applications

Venn diagrams are also useful in fields such as computer science, linguistics, logic, statistics, and teaching.

• Visualizing the hierarchies of computer languages

• Understanding how different languages are similar

• Testing the validity of arguments using Boolean statements that contain the conjunctions “or” and “and.”

• Comparing and estimating the chance of certain occurrences occurring

• Improving reading comprehension, such as when examining novels to see how people, ideas, themes, and places differ and overlap.

Advantages of Venn diagrams

A Venn diagram has the following benefits:

• It aids in the visualisation of concepts and relationships. 

For example, if two items, such as vehicles, each have 20 features but 10 different features, an illustration may help customers figure out which features the cars have in common faster than a spoken discussion.

• It reduces complex information to simple terms. 

When individuals are looking at statistics or different themes in a story, this is true. Venn diagrams frequently employ few words or short ideas to depict complex ideas.

• It aids in the retention of information. 

Colourful Venn diagrams help people identify ideas with the colours they employ. In other circumstances, drawing a Venn diagram assists people to assimilate knowledge and retain concepts more quickly.

Conclusion

A Venn diagram is a visual representation of relationships between things or limited groups of objects using circles. Circles that overlap have similar qualities to circles that do not overlap. Venn diagrams are graphic representations of the similarities and differences between two concepts. They’ve long been recognised as important educational tools. Venn diagrams have been employed in introductory logic curriculum and elementary-level instructional plans around the world since the mid-20th century.