venn diagrams explanation and free printable templates
Venn Diagrams: Explanation and Free Printable Templates
The usage of Venn diagrams in mathematics, statistics, science, and engineering is widely known. While Venn diagrams ensure an easier representation of facts, they also aid the user in visualizing them. This Buzzle article helps you understand Venn diagrams with some examples, and also furnishes you with some free printable templates of the same.
Three-circle Venn Diagram
Using Venn Diagrams in Logic
Syllogism in 'Categorical Logic' makes an interesting use of Venn diagrams. They have three categories or propositions, which consist of two premises and one conclusion. The conclusion is deduced from the two premises given. Venn diagrams are popularly used to test the validity of these syllogisms. With the help of three overlapping circles, the conclusion is tested by diagramming the premises on these representative circles.
Example
Major premise: All M are P.
Minor premise: All S are M.
Conclusion: Therefore, All S are P.
The above-mentioned example has been denoted by the mnemonic Barbara (AAA-1). All the aforesaid premises are 'Universal Affirmatives'.
![]()
![]()
Let's take a real-world example of the premises mentioned above.
All snakes are reptiles.
All cobras are snakes.
Therefore, all cobras are reptiles.
Let 'S' represent all 'Cobras', 'M' represent 'Snakes' and 'P' represent all 'Reptiles'. To test whether the syllogism's conclusion is valid, let's take help of a Venn diagram.
First, to represent, 'All snakes are reptiles', we shade out, that portion of circle M which is not in circle P. This indicates that all of circle M is in Circle P.
Secondly, to represent the minor premise, 'All cobras are snakes', we shade out that portion of Circle S which is not in Circle M.
To make it a valid syllogism, the conclusion should implicate into a result which is commonly said by the premises. Now, if we see the conclusion ' All cobras are reptiles' - all of Circle S should be in Circle P, and while diagramming the two premises, that portion of Circle S which was not in Circle P has been shaded out automatically. Thus, the Venn diagram proves our syllogism to be valid.
Three-circle Venn Diagram: Blank Template
Four-circle Venn Diagram
Using Venn Diagrams in Set Theory
Set theory makes wide use of Venn diagrams. It is easy to understand the union and intersection of sets with the help of Venn diagrams.
Example
Set A contains multiples of 2
Set B contains multiples of 4
Set C contains multiples of 6
Set D contains multiples of 8
Set A = {2,4,6,8,10,12,14,16}
Set B = {4,8,12,16,20,24,28,32}
Set C = {6,12,18,24,30,36,42,48}
Set D = {8,16,24,32,40,48,56,64}
![]()
The intersection of all the sets, can be easily displayed in the common space of all the four circles.
A ∩ B ∩ C ∩ D = {24}
![]()
Venn diagrams make understanding logic, math, and probability easier and more fun too. You can use the printable templates given here, to solve math problems using Venn diagrams. On a lighter side, you could use them to present ideas. For instance, success can be represented as an intersection set of passion, talent, and market demand. Or good business leaders can be represented as an intersection of sets representing people who dream big, and people who can take risks. To represent something funny, like 'all women love shopping', you can have a circle denoting 'all women' drawn inside a circle denoting 'people who love shopping'. Be it school science or real-world scenarios, Venn diagrams are of great help in representing data sets and explaining the relations between them.Four-circle Venn Diagram: Blank Template