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Venn Diagram Examples for Problem Solving.
Computer Science. Chomsky Hierarchy

Venn diagram going by such nicknames as “primary diagram”, “set diagram” or “logic diagram” is widely known. This kind of diagram shows all possible logical relations between a finite collection of different sets. These diagrams depict the elements as points in the plane as well as sets of the regions inside the closed curves. A “Venn diagram” consists of the multiple overlapping closed curves, which are usually represented in the circles, each of which represents a set. The points inside a curve labeled “S” represent all of the elements of the set “S” and the points outside the boundary represent all of the other elements, but in the set “S”.

In “Venn diagrams” the curves are overlapped in different ways, showing all possible relations between the existing sets. This kind of diagrams was invented in the year of 1880 in a paper work named “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings” by John Venn in the "Philosophical Magazine and Journal of Science" and they are used to teach elementary of the “set theory”, as well as to illustrate the simple set relationships in logic, linguistics, probability and computer science. Venn never used the term "Venn diagram" and he referred to his invention as “Eulerian Circles”. An “area-proportional” or “scaled” Venn diagram is the Venn diagram in which the area of each of the shapes is proportional to the number of elements which it contains.

Venn diagrams in general are very similar to the “Euler diagrams”, which were invented by Leonhard Euler in the 18th century. Baron has noted that Leibniz in the 17th century produced similar diagrams before Euler, most of which was unpublished. In the 20th century, Venn diagrams were better developed and in 1963 D. W. Henderson showed that the existence of an n-Venn diagram with n-fold “rotational symmetry” implied that n was a “prime number”, which means a natural number greater than 1 that has no positive divisors other than 1 and itself.

D. W. Henderson also showed that symmetric Venn diagrams exist when n is 5 or 7. In the year of 2002 Peter Hamburger found symmetric Venn diagrams for n = 11 and in 2003, Griggs, Killian and Savage showed that symmetric Venn diagrams exist for all other primes. Thus, rotationally symmetric Venn diagrams exist if “n” is a “prime number”. “Venn diagrams” and “Euler diagrams” were incorporated in the 1960s as part of instruction in so-called “set theory” as part of the “new math movement”. Since then, they have also been adopted in the curriculum of other fields.

A Venn diagram is built using a collection of simple closed curves in a plane. The principle of these diagrams is that classes (also known as “sets”) can be represented by regions in such relation to one another that all the possible logical relations of these classes (or “sets”) can be indicated in the same diagram. That is, the diagram initially leaves room for any possible relation of the classes. The actual or given relation within this diagram can be specified by indicating that some particular region is null or is not-null.

Venn diagrams normally comprise the overlapping circles. The inner part of the circle with the aid of the symbols represents the elements of the set. The exterior, though, implies elements that are not included into of the set. For example, in a two-set Venn diagram, one circle may represent the group of all objects made of wood, while another circle may represent the set of all tables. The overlapping region would then represent the set of all wooden tables. Any other shapes, but circles, can be employed as shown below by Venn's own higher set diagrams.

Venn diagrams do not contain the information on the relative or absolute sizes of sets and they are similar to “Euler diagrams”, as mentioned before. However, a Venn diagram for “n” component sets must contain all 2n hypothetically possible zones which correspond to some combination of inclusion (or exclusion) in each of the component sets.

The difference between the “Euler diagrams” and the “Venn diagrams” is that the “Euler diagrams” contain only the actually possible zones in a given context. In “Venn diagrams”, though, a shaded zone may represent an empty zone. At the same time in the “Euler diagrams” the corresponding zones are missing from the diagrams. As an example, you can imagine one set representing dairy products and another one – cheeses. In this case the “Venn diagram” contains a zone for cheeses that are not dairy products. Thus, the context cheese means some type of dairy product, the “Euler diagram” has the cheese zone entirely contained within the dairy-product one as there is no zone for non-dairy cheese. In this case the “Euler diagrams” are typically less visually complex than similar to them “Venn diagrams”, especially if the number of non-empty intersections is small.

Once you plan to draw any of the mentioned above diagrams, including the “Venn” ones, then you can find ConceptDraw PRO a very useful tool that allows to make any needed drawings within a short period of time having all of the necessary tools, such as design elements and symbols, which are all always available for ConceptDraw PRO users: basic in the application and all the rest needed are there in solutions, which can be always downloaded from ConceptDraw STORE or from this site. You can always draw any “Venn diagram” for a purpose of the problem-solving in computer science using the ConceptDraw PRO diagramming and vector drawing software extended with the “Venn Diagrams solution”. The “Venn Diagrams solution” can be always downloaded from the "What is a Diagram" area of ConceptDraw Solution Park on this site or from ConceptDraw STORE.

Venn Diagrams Solution

Example 1. Venn Diagrams Solution

The Venn diagram example below visualizes the the class of language inclusions described by the Chomsky hierarchy.

"Within the field of computer science, specifically in the area of formal languages, the Chomsky hierarchy (occasionally referred to as Chomsky-Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. The Chomsky Hierarchy, in essence, allows the possibility for the understanding and use of a computer science model which enables a programmer to accomplish meaningful linguistic goals systematically." [Chomsky hierarchy. Wikipedia]

Venn Diagram Problem Solving Example - Chomsky Hierarchy

Example 2. Venn Diagram Problem Solving — Chomsky Hierarchy

A graphical representation of the sets of languages included in the Chomsky hierarchy.

"The Chomsky hierarchy consists of the following levels:

  • Type-0 grammars (unrestricted grammars) include all formal grammars. They generate exactly all languages that can be recognized by a Turing machine. These languages are also known as the recursively enumerable languages.
  • Type-1 grammars (context-sensitive grammars) generate the context-sensitive languages. ... The languages described by these grammars are exactly all languages that can be recognized by a linear bounded automaton (a nondeterministic Turing machine whose tape is bounded by a constant times the length of the input.)
  • Type-2 grammars (context-free grammars) generate the context-free languages. ... These languages are exactly all languages that can be recognized by a non-deterministic pushdown automaton. Context-free languages – or rather the subset of deterministic context-free language – are the theoretical basis for the phrase structure of most programming languages, though their syntax also includes context-sensitive name resolution due to declarations and scope. Often a subset of grammars are used to make parsing easier, such as by an LL parser.
  • Type-3 grammars (regular grammars) generate the regular languages."
    [Chomsky hierarchy. Wikipedia]

Having ConceptDraw PRO software as well as ConceptDraw STORE one allows anyone who cares for their drawings to look not only nice but also smart and professional, to get the needed result in only a few hours or even minutes, depending on how familiar you are with ConceptDraw PRO.

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Process Flowchart

When trying to figure out the nature of the problems occurring within a project, there are many ways to develop such understanding. One of the most common ways to document processes for further improvement is to draw a process flowchart, which depicts the activities of the process arranged in sequential order — this is business process management. ConceptDraw PRO is business process mapping software with impressive range of productivity features for business process management and classic project management. This business process management software is helpful for many purposes from different payment processes, or manufacturing processes to chemical processes. Business process mapping flowcharts helps clarify the actual workflow of different people engaged in the same process. This samples were made with ConceptDraw PRO — business process mapping software for flowcharting and used as classic visio alternative because its briefly named "visio for mac" and for windows, this sort of software named the business process management tools. This flowchart diagram shows a process flow of project management. The diagram that is presented here depicts the project life cycle that is basic for the most of project management methods. Breaking a project into phases allows to track it in the proper manner. Through separation on phases, the total workflow of a project is divided into some foreseeable components, thus making it easier to follow the project status. A project life cycle commonly includes: initiation, definition, design, development and implementation phases. Distinguished method to show parallel and interdependent processes, as well as project life cycle relationships. A flowchart diagram is often used as visual guide to project. For instance, it used by marketing project management software for visualizing stages of marketing activities or as project management workflow tools. Created with ConceptDraw PRO — business process mapping software which is flowcharting visio alternative or shortly its visio for mac, this sort of software platform often named the business process management process flowcharts, flowchart symbols, process flow diagram, workflow diagram, flowchart maker
Picture: Process Flowchart
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Purchase Process Flow Chart,Receiving Process Flow Chart,Accounting Flowchart Example.

The purchasing process follows very specific guidelines and includes a purchasing cycle flowchart and receiving process flow chart. Common key elements of purchasing process. It is important to know how purchasing processes work and how each operation is done.Flowchart - purchasing process (receiving process flow chart)
Picture: Purchase Process Flow Chart,Receiving Process Flow Chart,Accounting Flowchart Example.
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Venn Diagram Maker

ConceptDraw PRO diagramming and vector drawing software extended with Venn Diagrams solution from the "What is a Diagram" area of ConceptDraw Solution Park is a powerful Venn Diagram maker. Create fast and easy your own Venn Diagrams to visualize: all the possible logical relations between sets, simple set relationships in logic, statistics, mathematics, sociology, marketing, summarize the status and future viability of a project.Venn Diagram Maker
Picture: Venn Diagram Maker
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UML Diagram

While developing software, it is very important to have a visual model, because it helps to represent the logic and the architecture of an application. Experienced engineers use UML diagrams to denote relationships between classes and their instances. UML is a general language for a set of diagrams like deployment diagrams, object diagrams or use case diagrams. This diagram represents UML class diagram used for a software system development using an object-oriented method. Class diagrams are categorized as static structure diagrams that depict the physical structure of a system. Class diagram divides a software system's structure into "classes". Classes are defined by the methods and variables of objects. UML Class diagram is used to depict relationships and source code dependencies between objects.UML Diagrams
Picture: UML Diagram
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Organizational Structure

Bureaucratic companies usually are characterized by a strict hierarchy and clearly defined responsibilities. However, sometimes organizational structure of a company reminds of somewhat tangled. To clarify it, you can create an orgchart that will represent the company as a tree with its' departments as branches. This organization diagram represents a tree-like organizational structure. This is a typical example of a top-level branches of the hierarchical organizational structure. This part of the tree shows heads of branches who are subordinated completely to the president. The information and solutions are distributed though a tree structure down to the company's departments. Each of the sub-division has its own structure that is reflected in the corresponding organizational chart. This orgchart diagram was created using the vector graphic library supplied with ConceptDraw Organizational Charts solution.Organizational Structure Solution
Picture: Organizational Structure
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Block Diagram

The vector stencils libraries: Block Diagrams, Blocks with Perspective, Callouts, Connectors, Raised Blocks from the solution Block Diagrams contain specific block diagram symbols such as arrows, input/output symbols, start/end symbols, processing symbols, conditional symbols, commenting symbols, callouts, connectors, etc. for ConceptDraw PRO diagramming and vector drawing software. The Block Diagrams solution is contained in a "What is a Diagram" area of ConceptDraw Solution Park. Use the libraries from the Block Diagrams solution to draw block diagrams for your business documents, presentations and websites in a few minutes.Block Diagram
Picture: Block Diagram
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Network diagrams with ConceptDraw PRO

Of course it is possible to keep network records in text documents, but it is very difficult to use them later. A more sound way to keep such documentation is to create a network diagram that might represent either logical network structure or physical. These diagrams are easy to understand and you will thank yourself later. There is a physical network diagram. It is a tool to represent, maintain and analysis of network equipment and interconnections. Network diagram depicts the actual network information in the attractive clear graphic form. One can learn here the LAN cable length, telecommunication type and carrying capacity. The diagram depicts servers, IP address and domain name as well. Also it shows location of hubs, switches, modems, routers, and other network equipment. The sets of special symbols and images delivered with ConceptDraw Network Diagrams solution are used to show network components. Symbols have a standard view. Therefore, various specialists can read the network diagram without any discrepancies.Network diagram
Picture: Network diagrams with ConceptDraw PRO
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Basic Flowchart Symbols and Meaning

While creating flowcharts and process flow diagrams, you should use special objects to define different statements, so anyone aware of flowcharts can get your scheme right. There is a short and an extended list of basic flowchart symbols and their meaning. Basic flowchart symbols include terminator objects, rectangles for describing steps of a process, diamonds representing appearing conditions and questions and parallelograms to show incoming data. This diagram gives a general review of the standard symbols that are used when creating flowcharts and process flow diagrams. The practice of using a set of standard flowchart symbols was admitted in order to make flowcharts and other process flow diagrams created by any person properly understandable by other people. The flowchart symbols depict different kinds of actions and phases in a process. The sequence of the actions, and the relationships between them are shown by special lines and arrows. There are a large number of flowchart symbols. Which of them can be used in the particular diagram depends on its type. For instance, some symbols used in data flow diagrams usually are not used in the process flowcharts. Business process system use exactly these flowchart symbols.Flowchart Symbols and Meaning, workflow diagram symbols, process flow diagram symbols
Picture: Basic Flowchart Symbols and Meaning
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Chemistry Drawings

ConceptDraw PRO diagramming and vector drawing software extended with Chemistry solution from the Science and Education area is a powerful chemistry drawing software that is ideal for quick and easy designing of various: chemistry drawings, scientific and educational chemistry illustrations, schemes and diagrams of chemical and biological lab set-ups, images with chemical formulas, molecular structures, chemical reaction schemes, schemes of labware, that can be then successfully used in the field of science and education, on various conferences, and so on.Chemistry Drawings
Picture: Chemistry Drawings
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Hierarchical Network Topology

This sample was created in ConceptDraw PRO diagramming and vector drawing software using the Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park. This sample shows the Hierarchical network topology. A Hierarchical network topology interconnects multiple groups that are located on the separate layers to form a larger network. Each layer concentrates on the specified functions, this allows to choose the right equipment for the layer.Hierarchical Network Topology
Picture: Hierarchical Network Topology
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