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# Venn Diagram Examples for Problem Solving

Sometimes the problems cannot be solved as easily as we want them to be, so for making it easier to understand them in order to simplify the tasks, it is better to create a diagram. In this way, with the help of a drawing, it can become clear what to focus on as well as what aspects to pay more attention to.

Having the examples of the problem-solving process in a way of a Venn diagram may lead to making it possible to create the needed scheme of what should be done as well as what work should be finished first within some project or an organization as a whole.

Any Venn diagram can also be called as a primary one. The other names for it are logic diagram, set diagram, etc. It is simply one of the so many types of the diagrams that are used for showing all the possible logical relations between some finite collection of a few or a lot of the different sets.

Example 1. Venn Diagram Problem Solving

The mentioned type of diagrams can be also used for depicting different elements in a way of the points in the plane as well as the sets in a way of the regions that can be found inside some closed curves. Any Venn diagram created with the help of the ConceptDraw DIAGRAM diagramming and drawing software may consist a lot of the overlapping closed curves such as circles, each of which is known for representing some set.

The mentioned points inside each of the curves are labelled with a letter “S” representing the elements of the set S in this way. At the same time, the points that can be found outside the boundary, are those which represent the elements which cannot be found in the “S” set.

In this way, the set of all the existing elements (which are known to be members of both sets S and T) can be represented in a visual way by the area of the overlap of the “T” and “S” regions.

In Venn diagrams the curves are usually overlapped in the way its creator wants them to be, showing all the possible relations in between the previously described sets. The mentioned “Venn diagrams” were conceived by John Venn in about 1880.

Since then, they are used for teaching the so-called “elementary set theory”. Besides, they can be also used for illustrating some simple set relationships in either logic, statistics, probability, linguistics or computer science, or both.

Any Venn diagram in which the area of each of its shapes seems to be proportional to the number of all the elements that it contains, is known to be called as a “scaled” or an “area-proportional” Venn diagram that is being constructed with the simple closed curves drawn in a plane.

The principle of all the Venn diagrams is that the sets (also known as “classes”) can be represented by regions in a special relation to one another. Due to such relation, all the possible logical relations of the mentioned classes can be indicated in the very same diagram showing the connections to each other.

In this way, the diagram leaves enough room for any possible relation of the classes to illustrate, and the given (or “actual”) relation can be after specified by indicating that some region is either not-null or null.

Example 2. Venn Diagram Problem Solving

Venn diagrams usually are those that comprise the overlapping circles and the interior of such circles can symbolically represent all the elements that the set includes. At the same time, the exterior is known to be representing those elements that are not members of the set and so they are not connected with it at all.

After being introduced by John Venn in 1880, the Venn diagrams were further developed in the 20th century. Thus, in 1963 D. W. Henderson showed that the existence of an n-Venn diagram that has n-fold rotational symmetry implied that n was a key number, called as “prime”. It was also showed that all symmetric Venn diagrams exist when n is either 7 or 5.

Venn diagrams are known to be similar to Euler diagrams, but still the first ones are more commonly used and many of those who made them know, that each of such diagrams for n component sets has to contain all 2n possible zones that are known to be corresponding to some combination of either exclusion or inclusion in each of the existing component sets.

It is also widely known that, to compare to the Venn diagrams, the Euler ones contain only the actually possible zones in some given context, but both Euler diagrams as well as Venn diagrams were incorporated as part of instruction in a so-called “set theory” in the 1960s as part of the new math movement. Since then, they have also been adopted in the curriculum of many other fields and nowadays they can be used for most of the needed problem-solving processes as long as there is enough information to add to them.

Example 3. Venn Diagram Problem Solving — BQP Complexity. The suspected relationship of BQP to other problem spaces.

In the Business Diagrams solution, there are the pre-made examples that can be always used for making the unique, great looking diagrams, such as the 2-set Venn ones of any needed colour, the 3-set one, the 4-set ones and the 5-set ones. Having the already previously created samples of the Venn diagrams can help any ConceptDraw DIAGRAM user make it possible to make the needed drawing within only a few minutes by editing the existing ones.

Taking this opportunity of using the already previously design diagrams, such as the Venn ones from the Business Diagrams solution, can simplify your work of the drawings and save your time. One of the examples, that is available for all the ConceptDraw DIAGRAM users is the “Venn Diagram — Internet Marketing Professions”. Next, the “Venn Diagram — Path to Sustainable Development” is another template of the Venn diagram created by using three circles where such notes as “Environmental”, “Social” and “Economic” are used.

### Example of DFD for Online Store (Data Flow Diagram) →

Structured-systems analysis and design method uses data flow diagrams to represent the process of data flowing through a system. Talking about this might be useless without a proper example of DFD for online store (Data Flow Diagram). This DFD example shows all the distinctness that a diagram can bring into a scattered data structure. Data flow diagrams are used to show how data is processed within some business processes. Making DFD is a common practice for business process modeling and analysis. This diagram represents the online store business flow. It describes inputs and outputs within online selling process and depicts the interactions between its participants. This DF diagram can be used by system analysts to create an overview of a business, to study and discover its inherent strengths and weak points.
Picture: Example of DFD for Online Store (Data Flow Diagram)
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### IDEF0 standard with ConceptDraw DIAGRAM →

The activity of any organization is more or less branchy network of processes. The description of these processes is a hard technical task which requires definite methodology and standards. According to the IDEF0 standard any process can be described in the form of a block (Activity Box) which has inputs and outputs. The process consists in transformation of inputs into outputs under the influence of the management and in the presence of necessary resources. Outputs of the given process later on can be either inputs for the next process or resources, or management means.
Picture: IDEF0 standard with ConceptDraw DIAGRAM
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### UML Class Diagram Generalization ExampleUML Diagrams →

This sample was created in ConceptDraw DIAGRAM diagramming and vector drawing software using the UML Class Diagram library of the Rapid UML Solution from the Software Development area of ConceptDraw Solution Park. This sample describes the use of the classes, the generalization associations between them, the multiplicity of associations and constraints. Provided UML diagram is one of the examples set that are part of Rapid UML solution.
Picture: UML Class Diagram Generalization ExampleUML Diagrams
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### Quality Project Management with Mind Maps →

The visual form of mind maps is helpful in all stages of quality management, from describing problem to describing and documenting a decision.
Picture: Quality Project Management with Mind Maps
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### How To Create Restaurant Floor Plan in Minutes →

As restaurant industry is growing rapidly nowadays, researches show that almost half of the adults have worked in a restaurant or a cafe. Moreover, many of them dream to start their own someday. Unfortunately, it takes a lot of time to write a business plan and to find a great location, although some know how to create a restaurant floor plan in minutes or how to plan budget effortlessly. Hiring employees can also cause a lot of headache, but this is crucial for further success, because every guest comes to restaurant for a good service and delicious food. It is also worth noting that restaurant concept is also important, because it defines target audience and influences the menu. This diagram represents the floor plan of an ongoing sports-theme establishment - restaurant, cafe, or other food service. A number of widescreen monitors installed along the perimeter provide visitors the opportunity to follow the course of a match from anywhere in the dining room of restaurant or cafe. The most of sports fans believe that food and alcohol is a big part of any sports show. That is why the dining room takes the most space - almost 60% of the total establishment space. Nearly all sports fans consume beverages while watching sports - beer, soda or water at least. Thus, the restaurant floor plan designers added a large lavatory there. Moreover, project developers considered unnecessary the gender division of such delicate place - perhaps they guess that only men are watching football, or believe that alcohol will eliminate the most of gender differences.
Picture: How To Create Restaurant Floor Plan in Minutes
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### Workflow Diagram →

Sometimes it's difficult to find a path in work processes or to understand the requirements, especially when you are a newcomer. To get your thoughts straight, create a workflow diagram, and put everything on it. This will not only help you to get into the workflow, but also show it’s weaknesses. This illustration captures the workflow process of payment an invoice for the electricity consumed by certain enterprise. It was drawn in ConceptDraw DIAGRAM using its solution for Workflow Diagrams. Making a workflow charts means that you need to depict consistently all processes engaged to the workflow process. Then, you should connect them with symbols meaning study and analysis. Next, add symbols of decisions. A work flow diagram made precisely and correctly can help to clarify your work flow to any person.
Picture: Workflow Diagram
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### Types of Flowcharts →

A flowchart is a simple but very functional tool when it comes to understanding a workflow or to removing unnecessary stages from a process. When drawing flowcharts, keep in mind that there are four common types of flowcharts, like document flowcharts and data flowcharts that show control over a data or document flow over a system. To show controls on a physical level, use system flowcharts. In addition, to show controls in a program, you can draw a program flowchart. This flowchart diagram represents the piece of an article editing process, that involves the author and editor. It was created using the Basic Flowchart notation that consists from the basic flowchart symbols. The start and the end of the process are indicated with "Terminator" symbols. The "Process" symbols show the action steps consisting from making edits and searching for a compromise, when the author does not agree with the suggestions of the editor. The "Process" symbol is the general symbol in process flowcharts. The "Decision" symbol indicates a branching in the process flow. There are two branches indicated by a Decision shape in the current flowchart (Yes/No, Disagree/Agree). This basic flowchart can be used as a repeating unit in the workflow diagram describing the working process of some editorial office.
Picture: Types of Flowcharts
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### Program Evaluation and Review Technique (PERT) with ConceptDraw DIAGRAM  →

Big and complex projects sometimes need some simplification of plans and schedules. That's why Program Evaluation and Review Technique was invented and first implemented in 1958. You can create PERT diagrams effortlessly with ConceptDraw DIAGRAM and share them with your colleagues. Program Evaluation Review Technique (PERT) is a method that is used to assess and analyze projects. PERT is a valuable tool for the project management practice. PERT gives an assessment and analysis of the time needed to the project completion. A PERT chart is a visual tool that delivers a graphical view of a project timeline. It is used to display the sequences and dependences of project tasks necessary to complete a project. ConceptDraw DIAGRAM delivers the possibility to build a PERT along with other diagrams applied to assist management process by using its Seven Management and Planning Tools solution.
Picture: Program Evaluation and Review Technique (PERT) with ConceptDraw DIAGRAM
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### Venn Diagram Maker →

ConceptDraw DIAGRAM charting and vector drawing software extended with Business Diagrams solution from the Management 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.
Picture: Venn Diagram Maker
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