Venn diagrams and Euler diagrams look very similar so it is understandable that many people find it confusing to identify the difference. Although both the diagram types rely on the set theory there are some subtle differences that make them unique. Hopefully, this article will clear your doubts about Venn diagrams vs Euler diagrams and I will provide a few examples to make it clearer.
Venn vs Euler: The Definition
What is a Venn diagram?
In the simplest terms, a Venn diagram illustrates the logical relationship between two or more sets of items. It visually represents the differences and similarities between the two concepts.
What is an Euler diagram?
An Euler diagram is another diagram that represents sets and their relationships. It’s similar to a Venn diagram as both use circles to create the diagram. However, while a Venn diagram represents an entire set, an Euler diagram represents a part of a set. A Venn diagram shows an empty set by shading it out, whereas in an Euler diagram that area could simply be missing altogether.
What are the Differences Between a Venn Diagram and Euler Diagram?
Both sets of diagrams are based on the set theory. A Venn diagram shows all possible logical relationships between a collection of sets. But an Euler diagram only shows relationships that exist in the real world.
While Venn diagrams and Euler diagrams are both tools used to represent sets and their relationships, there are some important differences between the two.
| Feature | Venn Diagram | Euler Diagram |
| Overlap | The overlap between two or more sets is represented by a shared region in the diagram. | Can use overlapping or nested shapes to represent the relationships between sets, and may not have any shared regions at all. |
| Completeness | Designed to be complete, meaning that they show all possible relationships between sets. | Can be partial or incomplete, meaning that they may not show all possible relationships between sets. |
| Expressiveness | Limited in their expressiveness, as they can only represent set relationships in terms of union, intersection, and difference. | Can use overlapping and nested shapes to represent a wider range of relationships and dependencies between sets. |
| Complexity | Can become complex and difficult to read when representing relationships between more than three sets. | Can be designed to handle more complex relationships and can be easier to interpret in these cases. |
In general, Venn diagrams are ideal to visualize simple set relationships and can be useful for teaching basic concepts in set theory. However, Euler diagrams are more flexible and versatile, therefore they can be used to visualize a wider range of relationships between sets. This makes them useful for more complex situations and applications.
Venn Diagrams vs Euler Diagrams Examples
Let’s start with a very simple example. Let’s consider Animals superset with mammals and birds as subsets. A venn diagram shows an intersection between the two sets even though that possibility doesn’t exist in the real world. Euler diagram, on the other hand, doesn’t show an intersection.
Now let’s take a look at a bit more complicated example involving a pack of cards. Again it is important to keep in mind the difference between the two diagram types, all possible combinations vs real-world combinations. Let’s take cards as the superset and black cards, red cards and diamonds as the subsets.
As the above example shows, Venn diagrams show four intersections that don’t have any data because it should show all possible combinations.
There are various methods to convert Venn diagrams to Euler diagrams and vice versa. Check out this great wiki article about Euler diagrams which explains some methods you can use to convert Venn diagrams to Euler diagrams. I hope the above examples helped you clear your doubts about Venn diagrams vs Euler diagrams. If you have any questions feel free to ask in the comments section.
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All we really need is a Venn diagram that shows “all possible logical relationships that could ever exist” and where we place some kind of ‘currently empty’ symbol inside any area that we think is currently empty in the real world.
This would make all Euler diagrams redundant.
In your first example, the Venn diagram is wrong (based on your definition) because it is not logically possible for anything to go into the intersection. An animal can be either a bird or a mammal but it is not logically possible for it to be both.
You could correct this example by changing ‘mammals’ to ‘creatures with antlers’. Then if in the future someone were to breed a bird with antlers, it would then make the Euler diagram incorrect.
Your second example lacks clarity. I assume your ‘red card’ and ‘black card’ classifications mean the colour of the suit symbol on the card (note that J, Q and K cards often contain many colours).
I wondered about creating a new suit with a mixture of red and black. If your classification means the colour of any part of the suit symbol then your example is correct.
However, if ‘red card’ means an all-red suit symbol then such a card could not go in the intersection because it cannot go in the ‘red’ set or in the ‘black’ set as it is neither. A card cannot be all-red and all-black at the same time.
An earlier comment said that a Venn diagram was useless because it contains info that does not exist in the real world. I think this view was formed from inspection of your examples. A Venn diagram that shows “all possible logical relationships that could ever exist” does contain valuable information.
So a Venn diagram is just a poorly made, useless Euler diagram. A diagram that contains “info” that doesn’t exist in the real world is a useless diagram. My Euler diagram shows a big circle that says “Useful diagrams”, taking up this whole circle is another circle saying: “Euler diagram”, outside of these is a circle called “Useless diagrams” with a circle inside saying “Venn diagrams”, it does not overlap with the “Useful diagrams” circle, tah dah!
Rambo
Actually Venn diagrams can be very useful in exploring combinations you haven’t considered before.
To use an example: Pokemon!
Say you have fire, psychic and flying types, and you are making new pokemon for a new game. You might want to make some new combinations that haven’t existed before. You take all the pokemon, put them in a Venn diagram with these 3 categories of types: Moltres is flying and fire, easy. But are there Psychic Flying pokemon? (turns out yes – Xatu) Or Psychic Fire pokemon? (turns out yes, Delphox)
In this way you can find options for combinations you haven’t had before. (And I’m pretty sure this happens regularly in Pokemon every time they add a new category of type).
Can you please help me solve these questions:
(1)Let U be the students in the class today. define a subset A of U based on some quality or characteristic. (something other than gender). clearly define A in words. You do not need to place people in set A by name. let F= females and M= males.
solve:
A=?,
A’=?,
AnF=?
F’=?,
MUF=?,
MnF=?,
n(U)=?,
n(F)=?,
n(M)=?.I need tour help with these question:
(2) Make up a real world example where ACBCU. define A, B, and U and draw an euler diagram.
I’m still confused, but I will try hard to learn. Thanks bro, have provided information and a little bit about this picture
Some A are B,No B are C…concl: All C being A is possibility
Hello sir having a doubt pls explain it for me….stmt:some A are B,All B are C….CON:All A being C is the possibility……..