What is a Venn Diagram and When to Use It?

What to expect for 11 plus?

Like them or loathe them but Venn diagrams are a topic that has come up time and time again in the 11 plus exams and are an important topic for your child to know about.

Venn diagrams are widely used in schools to sort data. In business, Venn diagrams are used to check valuable data that can benefit the company. Like any other diagram, Venn diagram has its unique feature that we need to comprehend so we can better read and analyse the data being presented in the diagram.

This blog post will explain in length what a Venn diagram is and when to use it. We will also explain how to make one. 

What is a Venn Diagram?

A Venn diagram is a kind of pictorial organiser. They are used for organising complex relationships visually. They allow abstract ideas to be more precise and visible. 

Venn diagrams are primarily used as a thinking tool, but in actuality, they can also be used for assessing things.

Venn diagrams use overlapping circles or other shapes to display the logical relationships, similarities, and differences between two or more set of items. It’s not required to use circles, but more often than not, it is the most convenient shape because circles can overlap easily. 

Each shape (in this case, each circle) represents some entity or “sets.” The features or characteristics the sets have in common are placed where the shapes overlap. The items or features unique to each set are written in the non-overlapping part of their respective shapes. 

If all the features of one set are among the features of another set, the entire shape of the first set is contained within that of the second set. 

Also called Logic diagrams or Set diagrams, Venn diagrams are extensively used in different fields, such as linguistics, business, statistics, logic, mathematics, teaching, logic, and computer science. 

You may have encountered them in school as you study logic or maths, and that’s because the Venn diagram became part of the “new math” curricula in the 1960s. 

With the advancement in technology, Venn diagrams are now usually presented in 3D presentations. What’s really great about the Venn diagram (compared to the others) is that it allows the viewers and users to visualise data clearly and powerfully. That explains why Venn diagrams are widely used in reports and presentations. 

Regarding the effectiveness of Venn diagrams, here’s what Robert M. O’Brien of Department of Sociology at the University of Oregon wrote:

“Venn diagrams are used to provide an intuitive understanding of multiple regression analysis and these diagrams work well with two variables.”

“The use of Venn diagrams has been suggested in the literature because they allow students and researchers to see diagrammatically many of the key components in multiple regression.” 

Venn diagrams, at a basic level, are simple visual representations of the relationship that exists between two sets of items or things. However, they are more complex in orientation and application. 

Venn diagrams are now popularly used to illustrate ideas, concepts, and groups. They are considered as trademark tools for teaching basic logic and math. 

The History of Venn Diagram

Venn diagrams have long been known for their effectiveness and usefulness on an educational level. Since the 20th century, they are being used as a part of the introductory logic curriculum (more of this later). 

John Venn, a British logician, introduced Venn diagrams in the 1880 Philosophical Magazine and Journal of Science with a title On the Diagrammatic and Mechanical Representation of Propositions and Reasonings. Hence, the diagram was named after him. 

Venn studied and taught probability theory and logic at Cambridge University. This is also where Venn developed his method of using diagrams to represent set theory. Venn published The Logic of Chance, a book that explained the frequency theory of probability. 

Venn gave a clarity to the popular educated assumptions by establishing that probability should be accepted based on the regularity that something is predicted to happen or occur. Venn also developed more apprehended George Boole’s theories in his 1881 book, Symbolic Logic

However, the genesis of this type of diagram actually dates back to the early 1200s. Ramon Llull, a philosopher and logician, used a diagram similar to that of Venn’s — this is according to M.E baron in his 1969 article. She also credited Gottfried Wilhelm von Leibnitz, a German mathematician and philosopher, for introducing similar diagram in the late 1600s. 

In the 1700s, Leonard Euler, a Swiss mathematician, introduced what came to be known as the Euler Diagram, which is the forerunner of the Venn Diagram. 

You’ll be surprised to know that even John Venn referred his diagrams as Eulerian Circles. It was only in 1918 that his diagrams were known as Venn Diagram when it was presented in the book A Survey of Symbolic Logic by Clarence Irving Lewis. 

Venn Diagrams continued to improve over the years. In 1963, D. W. Henderson showed that symmetric Venn diagrams could be used to examine prime numbers. 

Venn diagrams, along with Euler diagrams, were so significant that they were incorporated as part of instruction in set theory as part of the 1960’s new math movement. 

The Benefits and Purpose of Venn Diagram

Venn diagrams can be used in various fields for learning and analyzation. Below are the purpose and benefits of the Venn diagram:

Helps organise information

Venn diagrams help organise information between sets of items, including differences and similarities. Both professionals and students can use Venn diagrams to think through the logic behind a concept or to see the relationships for visual communication. 

To compare choices between two or more sets

Venn diagrams can help you see clearly what the sets have in common and what makes them unique. This is applicable, especially if you’re thinking about buying a product or service. Venn diagram can help you filter the pros, cons, and the commonalities between two or more products. 

To solve difficult math problems 

If you’re a mathematician, Venn diagrams can help you solve complex mathematical problems.

Take for example, Peter Hamburger, who found symmetric Venn diagrams for the prime number 11. In 2003, Griggs, Killian, and Savage also showed that symmetric Venn diagrams exist for all other prime numbers. 

Quick fact: prime numbers are numbers indivisible by other numbers except 1 and the number itself, like 7, 11, 13, etc. 

To compare data between sets

Another purpose of Venn diagrams is to find connections and predict the probabilities of certain events. 

To find the reason behind the logic 

Venn diagrams are used to find the logic behind equations and/or statements. For example, the diagram is used to find the Boolean logic, a form of algebra that’s centred around three simple words (known as Boolean Operators): “or”, “and”, and “not”.

Venn Diagram in Different Industries

Venn diagrams are used widely to present sorted data. They’re used in different cases and industries.


Venn diagrams are used to identify the validity of certain arguments and conclusion. In deductive reasoning, for example, if the propositions are true and the argument form is correct, then the conclusion is true. To elaborate, if all cats are animals, and our pet Shelby is a cat, then Shelby must be an animal. If assigned to variables, let’s say cats are A, Shelby is B, and animals are C. In an argument form, we’d say:

All A are C. B is A. Therefore, B is C. A diagram in logic similar to Venn diagram is called a Truth Table.

In there, the variables are placed into columns to analyse what’s logically valid. Another similar diagram, the R-diagram or Randolph diagram (named after John F. Randolph), use lines to define the logic behind sets. 


Educators use Venn diagrams to help their students improve their reading comprehension. The students can use the diagram to compare the ideas they’re reading about. 


In business, Venn diagrams are used to compare products, processes, services, and pretty much anything that can be represented in sets. Venn diagrams are also an effective tool for illustrating comparisons and commonalities. 


Venn diagrams are being used to study and analyze the similarities and differences among languages. 

When to Use a Venn Diagram

Venn diagrams can be used when comparing and contrasting groups of things. They are useful and effective for formative assessment.

Formative assessment refers to a wide array of methods that educators use to conduct in-process evaluations (or assessments) of student comprehension, learning needs, and academic progress during a class, unit, or course. 

Why, you ask?

Venn diagrams can be used to generate engagement, participation, and discussion. What’s more, they provide educators with information about the thinking of the students. 

Venn diagrams can also be used in science as they are helpful for easier classification. 

But how do you read a Venn diagram?

If you need to interpret a Venn diagram, here are the things you need to do:

  1. Ask questions about the commonalities and differences that the Venn diagram presents.
  2. Provide true or false statements. 
  3. Then, discuss or ask questions about the two sets. For example, students may be able to say that whales have similarities to fish, but are not fish because they don’t lay eggs or have scales. 
  4. If appropriate, ask questions that motivate students to create generalisations. 

How to Make a Venn Diagram

To create a Venn diagram, the first step is to decide what your topic is or what to compare. Write a descriptive title at the top of the page. 

Then, create a diagram. Make circles for each subjects; each should overlap at least one other circle. You may also use other shapes, but circles are usually used because they overlap much easier. 

Next, label each circle. You may place the topic or subject of each circle near or inside the shape. Do not write the topics/subject inside the neighbouring circles to avoid confusion.

It would be helpful to change the font style and colour of the topics/subject to maintain clarity and to make them easily distinguishable. 

Inside each circle, write down the differences in the subjects. Place the characteristics that are unique to that specific to the topic, subject, or idea. 

Within the space where the circles (or other shapes) overlap, write down their similarities. 

Here’s an example:

As per the example above, listed inside the shape of FISH are the unique characteristics of the fish. Within the other circle are the unique features of whales. Inside the spaces where the two circles overlap are the characteristics that both species (fish and whales) have in common. 

The shapes of a Venn diagram can be more than two. 

Venn Diagram Glossary

Here are some of the words you will encounter with Venn diagrams. 


Set(s) is/are a collection of things. The sets could be anything (be in for business, mathematics, linguistics, computer science, etc.). The things may be be called objects, items, members, or other terms similar to these. 


Union refers to all items in the sets. 


Also called subset, the intersection is the items that overlap in the sets. 


These are everything that aren’t in the intersection. Simply put, these are the differences of the sets.


This refers to everything that is not in the set. 


Relative complement refers to things or items in one set but isn’t in the other. 


Scaled Venn diagrams are circles or any other shapes with sizes proportional to their representation of the whole. It is also called Area Proportional. 


This refers to the shape formed from the intersection of three circles or shapes, such as that of a Venn diagram. 


Set notations are the concepts being illustrated in Venn diagrams that are usually expressed in mathematical notations. The sets and subsets are represented by brackets, the unions by a u-like symbol, and the intersections by an upside-down U symbol. 


Set theory is the longstanding branch of math that deals with sets. Over 30 symbols are being used in set theory, but there are three common symbols that will teach you the basics — Union symbol (u), intersection (∩), and complement Ac. 


How To Choose The Best 11+ Tutor

Preparing for the 11+ is nerve-wracking, especially for those who wish to enter grammar schools. 

Independent and grammar schools have limited places, and thousands of students will have to compete with each other to fill the places.

This is the reason why personal tutors are in high-demand in the market. Agencies and private tutors all promise the same thing: to give children the best chances of passing the 11 plus entrance exam.

But because of the ever-increasing number of tutors and tutoring companies, picking the best 11 plus tutor becomes a rather tricky task. 

So how do you choose the best 11 plus tutor? How much does it cost? And is it even worth it? These questions will be answered in this blog post. Read on. 

Types of Tutor

It’s worth noting that there are different types of 11 plus tutor. The sort you pick will depend on the availability in your area, and of course, your own preferences according to your child’s needs. 

  • Independent tutors work locally and tutor children on a one-on-one setting or in small groups. The teaching session is usually held in the child’s home. Independent tutors are often qualified teachers who are on a career break or have retired already. Some are students. 
  • Online tutoring is usually on online messaging platforms such as Skype or any other telecommunications applications. This is the best option for pupils to be tutored remotely.
  • Tutoring centres are companies or agencies that employ several tutors. They can be locally-based and usually teach children in groups. Some prefer tutoring centres over private tutors because they build a small classroom atmosphere, so the environment is less intense for children. 

How to find an 11+ tutor 

So how do you actually find the best 11 plus tutor? A good place to start is by contacting The Tutors’ Association. This professional organisation is connected to hundreds of credible freelance tutors and tutorial companies, although some of them work in London only. 

Another way to find the best 11 plus tutor is by asking your friends, family, and parents of Year 7 children who have successfully passed the 11 plus exams. We could all agree… word of mouth recommendation is still the best way to find the best person for the job. 

The best tutors (whether independent or agency) are usually the ones who are experienced and knowledgeable. 

If you can’t find a locally available tutor, you may want to consider online tutoring. Online tutors are unlimited by location, but of course, you’d want to select a tutor who is immersed in the UK system. 

Well-respected tutoring companies will always pick credible and reputable tutors. They will also monitor the tutors’ professional success and progress. Tutorial companies should ensure all in-house tutors have a DBS check. So when looking for tutoring companies, look for members of The Tutors’ Association (TTA). 

If you prefer hiring independent tutors, make sure to ask for their DBS checks and references. 

It doesn’t hurt to ask the school you intend to apply to about how best you can prepare your child for the 11 plus exam. You can ask the school for sample 11 plus exam papers, or you can get it from their official website (if available).

A credible tutoring company usually has excellent sources to stimulate the child’s interest in learning all the while preparing him or her for the 11 plus exam. 

Sample exam papers will give you a good idea whether the standards of the school is within your child’s reach. Practice is important, and tutors can help your child develop a technique so they can enhance their memory, thinking ability, and reasoning.

Choosing a tutor

There is no independent accreditation or rating system for tutors. So you may need to interview them, get as much information about them, take up references, and get recommendations to ensure you’d pick the best 11 plus tutor.

But most importantly, you need to ensure that your child feels right with the person once the session starts. 
Here are other factors to consider when selecting an 11 plus tutor. 

  • Experience

Knowing the tutor’s experience at getting children into grammar schools is really important. Check whether the tutor or tutoring company has experience in coaching students in all of the elements of the tests.

If the 11 plus exam format has changed in your area, make sure the tutor knows about the latest changes.

But don’t close your doors to new tutors that may have more dynamic and interesting approach to children compared to matured tutors that have traditional coaching methods. 

  • Qualifications

Again, tutors don’t have rating systems, and they don’t need formal qualifications, but you’d feel more comfortable if yours have them.

For example, if reading and comprehension is your child’s weak point, you might want to select a tutor that’s good at reading and can help your child to improve his comprehension. 

  • Pass rates

Ask the tutor what percentage of his/her students have passed the 11 plus exam over the past few years. It’s best to get references from other parents whose children have been tutored by your potential tutor. 

  • Methods

Do you want your child to engage in a one-on-one tutor? Or do you want him/her to get involved in a small group? How often do you want your child to be tutored? It’s important to align your child’s needs with the tutor’s method of teaching. 

  • Location and cost

This may seem like a small factor to be concerned about, but these are important considerations, especially if you will be committing to a long-term tutoring programme. For example, single mums who don’t drive would prefer tutors who are willing to come to their house.

And of course, select a tutor that fits your budget. Again, not all expensive tutors are the best. Look for a tutor that prices reasonably. 

Does the tutor know the selection process in your area? 

It’s easy to assume that a tutor in your area or county knows the requirements of 11 plus, but sadly, that’s not always the case. You can find out what the tests will consist of by contacting the school or your Local Authority. 

Does the tutor have relevant qualifications? 

A credible tutor has teaching certificates or other academic certificates. Not all tutors are trained teachers, but anyone teaching a child should have a good academic history or background. Also, a tutor should have completed a Criminal Records Bureau (CRB) check within the last 5 years. He or she should be willing to show you their clearance form. 

A recent CRB check is really important, especially if your child is going to have a one-on-one session with the tutor. Do not accept any excuses.

But just because a tutor has a CRB check doesn’t mean you have to necessarily pick them. If you don’t (or your child) feel comfortable about their attitude toward your child (on their first meet or any time later on), you should look for another tutor immediately. 

You should pick a tutor that knows how to handle your child. For example, if you wish to interview the tutor before hiring him, you may want to ask about how he handles students and what he does to make learning fun.

You may also ask about what his techniques in dealing with bored and uninterested students. 

What is the cost? 

Independent tutors usually charge £17 to £25 per hour for individual tuition.

The cost varies depending on your area and the tutor’s popularity and experience. In-demand tutors can charge as high as £80+ per hour. Group tutoring is generally priced two-thirds the price of private sessions. Meanwhile, online tutors usually charge £15 per hour. 

Most tutoring centres charge a monthly fee, which can vary between £50 and £120 per month, usually for two sessions per week. 

Remember, charges vary among tutors. But just because it’s expensive doesn’t mean it’s necessarily the best one. Some tutors will ask for payment on a weekly or semi-weekly basis, while others ask for large amounts in advance.

If a tutor asks you for full payment in advance, you should consider it very carefully before shelling out cash. If your child does not get on with his tutor, or it becomes clear that your child does not have the potential to qualify the 11 plus exam, you will just lose a huge amount of money. 

Will the tutor suit your child?

One of the most important factors in selecting an 11 plus tutor is to consider how they will get on with your kid. Some parents like traditional and mature tutors with broad experience, while others prefer young and dynamic tutors who can motivate their kid.

You must also carefully consider whether you prefer a female or male tutor for your child. In regards to tutoring centres, consider if you want your child to see the same person for every session. 

Before committing to a tutor, it’s best to have your child meet them. A couple of trial sessions is a great way to see how’d the tutor and your child get along. Remember, trial sessions may or may not be free. Seeing your child with the tutor is the best way to see if they are best for each other. 

Hiring a tutor for your child gives them a sufficient advantage over others. If your child is at prep school yet, getting a tutor is probably unnecessary.

Most prep school students hate it anyway. However, if your child is at a state primary, it makes sense to find a good, experienced tutor who will make sure that your kid is equipped when competing against those who are also prepped for the 11 plus exams. 

The tutor can help your child focus in areas that they find difficult. 11 plus exams are usually consists of English (comprehension and creative writing), Mathematics (numerical reasoning and standard math problems), verbal reasoning, and non-verbal reasoning.

If in any way your child struggles in one or more of these areas, a tutor can surely help. 

What feedback will they give you, and how often?

Regular feedback is vital. It lets you see your child’s real progress and chances of succeeding the 11 plus exam. It will also help you plan your child’s school options accordingly.

A good tutor will not sugarcoat his feedback and will be frank with you at all times. They may tell you if your child is likely or unlikely to pass. 

If it becomes clear that your child needs extra work to pass the 11 plus exam the tutor should explain that to you.

They may also suggest that the will not coach your child any further. It’s fair to think that the tutor is protecting their pass-rate by doing that. But a good tutor should not be more concerned about their pass rate.

It’s likely that they do not wish for you to spend more money unnecessarily or give you or the child false hope about their chances of passing the 11 plus exam. 

A good tutor will help you make the decision to stop tutoring and will help you manage your child’s emotions about it. 

In case your child isn’t equipped yet to ace the 11 plus exam, you should always have a Plan B. 

Monitor your child’s progress

When you’ve already chosen a tutor, you will need to ensure that your child is making great improvements with them. It’s not so much to ask for a report after every six or seven sessions.

You may also want to talk to the tutor about the test scores of your child — whether they’re improving or plummeting.

Speak to the tutor and ask them about the areas that your child struggles with. You should also try to listen to some tutoring sessions as well. You’ll be the judge of whether your child is learning and participating.

I cant afford a tutor, what do I do?

For a lot of parents, it’s very expensive to hire a one to one tutor, especially when you consider all the other expenses of having a child. This is one of the reasons that we developed KidSmart.

Our app is aimed at helping children prepare for their 11+ in just 20 minutes a day. Our app even has on-demand tutors within the app, so if your child gets stuck they can get real feedback from tutors.

This may be a more cost effective approach for parents who can’t afford weekly tuition sessions.