Euler diagram: examples and opportunities

Mathematics is an abstract science if you move away from the basic concepts. You can clearly depict the basic operations that are the basis of mathematics on a pair of apples, but as soon as the plane of activity is expanding these facilities are not enough. Have you ever tried to represent operations on infinite sets with the help of apples? Of course not. The more complex the concepts with which the math operates become, the more problematic it seems to represent them graphically. But on April 17, 1707, there was born Leonhard Euler - a scientist who had a unique ability to build transparent logical algorithms, cutting off all unnecessary. It was he who suggested the use of a graphical representation of operations of sets. Euler diagrams are a great solution to any, even the most difficult task, and most importantly - they can be represented graphically.

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What is the essence of this?

Euler diagram - a visual representation of logic operations that are based on the basic concepts of Boolean algebra.

• The sets A and B exist and are not empty, then the operations of
  intersection, union and negation are defined for them.
• The intersection of sets A and B is a set of all elements from set A
  and set B.
• Union of sets A and B is a set of all elements from set A or set B.
• Negation of A – is a set of all elements that set A doesn’t include.

The main features of the Boolean algebra

The sets A and B exist and are not empty, then:

• for the intersection and union of sets A and B​ the commutative law is
  used;
• for the intersection and union of sets A and B associative law is
  used;
• for the intersection and union of sets A and B the distributive law
  is used;
• negation of the intersection of sets A and B are the intersections of
  negations of A and B;
• negation of the union of sets A and B is the union of negations of A
  and B.

But the most important basic rules which are used in various fields of life are:

Let's talk about the use of Euler diagrams in our life.

Searching for colleagues

Often the biggest problem for all employers is to find a suitable employee, and there are so many criterions that often a lot of mistakes occur. So many entrepreneurs and Human Resources Departments interview their future employee using a simple diagram of Euler, which allows to fully assessing the future perspective of the employee and his professional qualities.

Management and marketing

The most commonly Euler diagrams are used by these fields, as their specificity requires a constant search for product variants that satisfy the set criteria. In order not to use bulky tables and make hundreds of lists, employees of these spheres began to use the most convenient method, an example of a diagram might look like this:

Medicine

Very often, the various medical institutions create their own infographics in the form of diagrams of Euler. They use this method due to its convenience for patients' and the readers of medical publications perceptions and also allows to present large amounts of information in summary form.

And, of course, Euler diagrams are very popular on the Internet, their use is quite multifaceted - from the usual fun charts:

To the various diagrams, which are used for studying and generalization of knowledge and used by various online courses and schools:

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Prospects of the work of Leonhard Euler are considered the basis of modern mathematics, but now they are successfully used in various fields of human activity, because they are compact and at the same time may contain a lot of information, have a simple logic of its creation that is clear for every person and is really pleasing to the perception.

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