Euler Diagram

What is Euler Diagram?

Euler diagrams are a common notation for displaying information about sets and their relationship with each other. They are often drawn as groups of (potentially interlinking) closed curves. These diagrams permit some omission of set interactions, allowing them to take advantage of the spatial qualities of containment and disjointness of curves.

These diagrams are useful in various applications to represent set-theoretical data, including visualizing statistical data, building the foundations for diagrammatic logic, software engineering, and displaying the results of database search queries. However, these methods can only generate diagrams for a limited portion of all conceivable abstract descriptions.

• An Euler Diagram is a visual or diagrammatic representation of sets and their interactions with each other. They are made up of simple closed curves in the plane (typically circles) that represent sets.
• Leonhard Euler, a Swiss mathematician, created the concept.
• They have a lot in common with Venn diagrams, but both have subtle differences.
• They are a natural way to represent data in set theory. Visualizing statistical data, creating the groundwork for diagrammatic reasoning, software engineering, and showing the results of database search queries are all Euler diagram examples of their utility.

Euler Diagram Explained

An Euler diagram is a representation of closed circles or curves that divide the plane into separate but connected subsets. They are called regions, each of which is surrounded by a set of curves. The common Euler diagram examples show set-theoretic relationships, with each curve representing a set and each region representing the intersection of several sets. Representations created through the online Euler diagram maker can have curves of any geometric shape. The diagram's value lies in how the curves overlap, not in their sizes or shapes. Therefore, set-theoretic interactions (intersection, subset, and disjointness) relate to the spatial relationships between the areas enclosed by each shape.

Swiss mathematician Leonhard Euler (1707–1783) provided the world with the idea of Euler diagrams, Eulerian circles, and Euler's constant. Here, each curve divides the plane into two zones or regions. The inside parts of the depiction represent the elements of the set, and the outside part represents the elements that are not part of these. Curves that do not have any common elements do not overlap and are the disjoint sets. Those sets that intersect have common features. At the same time, a curve that is completely inside another is its subset. Individuals can use an Euler diagram generator to get a basic idea of how the diagrams look.

Steps to Create Euler Diagram

These diagrams are useful to arrive at conclusive logical reasoning. In these premises, method for determining the correctness of arguments in which the terms "all, some, and no" appear. Here, the first step shall be to create a diagram for the first premise. Next, a second premise shall be drawn on the top of the first premise. An Euler diagram maker helps to easily create these diagrams thanks to the advancement of technology. And now, one can make the conclusions. However, the argument is valid if and only if each and every conceivable diagram depicts and matches the argument's conclusion. If even one conceivable diagram contradicts the ending, the conclusion isn't true in all cases, and therefore, the statement is incorrect.

Example

Given below are some arguments to be determined whether valid or invalid.

• All genius who sing cannot read.
• All genius who cannot read is ineligible for studies.
• Therefore, All genius who sings is ineligible for studies.

The first step would be to create an Euler diagram for the premise of the first argument.

This will be:

The next step is to create a diagram of the premise for the second argument, and the only logical conclusion is:

Therefore, the argument "All genius who sings is ineligible for studies" is valid.

Euler vs Venn Diagram

The concepts of the ''Euler diagram" and ''Venn diagram'' can get confusing. However, in reality, the latter is sort of a subclass of Euler diagrams. Unlike Venn diagrams, which must show all potential set intersections, the other only needs to represent a subset of them.

As part of the 1960s new math movement, Venn and Euler diagrams were used to teach set theory. The latter depict set relationships between circles regarding inclusion and exclusion relations. In addition, it represents emptiness either by shading or eliminating that region due to its absence. On the other hand, Venn diagrams contain a fixed circle configuration and depict set relationships by specifying that dark portions symbolize the empty set.

Unless their labels are in the crossing circle, overlapped circles in Venn diagrams do not necessarily show commonality between sets but rather a probable logical relationship. That is, they contain all the possible zones of overlap between the elements representing the curves. Few differences such as these differentiate the two topics; however, it cannot be denied that they share a lot more in common.

Frequently Asked Questions (FAQs)

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This is a Guide to Euler Diagrams. We explain the steps to create Euler diagram along with example & its differences with Venn diagram. You can learn more from the following articles –

• Fishbone Diagram
• Excel Venn Diagram
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