Relation based Venn diagrams

Questions on this topic check a candidate’s ability to find relation between given group of items and illustrate that diagrammatically.

So, let us learn how to represent a given relation in the form of Venn diagram.

In general you may encounter any of these 10 types of relations.

Relation Type 1

One class (or set) completely belongs to the other class and so on.

For example, Rajasthan is a state inside India. Venn diagrams

Relation Type 2

There is no relation between the given classes (or sets), i.e. no elements are common.

For example, India and France are two separate countries. Venn diagrams

Relation Type 3

No one class completely belongs to the other class but they are partly related to each other, i.e. few elements are common among them.

For example, India has some Hindus.
Venn diagrams All Indians are not Hindus. Also, not all Hindus live in India. So, there is an overlap between the two set of people, but none of them lie completely inside the other.

Let’s consider another example:
Venn diagrams The logic we applied to Indians and Hindus, can be applied to Indians and Jews too. But note that, there is no relation between the Hindu set and the Jew set (as no Hindu can be a Jew and vice-versa).

If there is an overlap between all the three sets then we get the next relation type.

Relation Type 4

All the three separate classes are partially related to one another.

For example, the classes of Indians, Scientists and Teachers.
Venn diagrams It means that:

  • Some Indians are scientists, some are not. Similarly, some scientists are Indians, some are not.
  • Some Indians are teachers, some are not. Similarly, some teachers are Indians, some are not.
  • Some teachers are scientists, some are not. Similarly, some scientists are teachers, some are not.

Relation Type 5

Two classes are partly related to each other and the third class is entirely different from these two.

For example, the classes of Lawyers, Professors and Monkeys.
Venn diagrams It means that:

  • Some Lawyers are Professors, some are not. Similarly, some Professors are Lawyers, some are not.
  • But no Monkey can be a Lawyer or a Professor.

Relation Type 6

One class belongs entirely to the second class while the third class is entirely different from the two.

For example, the classes of California, U.S.A. and Germany.
Venn diagrams It means that:

  • California is a state entirely inside U.S.A.
  • Germany is a separate country from U.S.A.

Relation Type 7

One class belongs entirely to the second class and the third class is partly related to the second class.

For example, the classes of Herbivores, Carnivores and Cows.
Venn diagrams It means that:

  • Some Herbivores can be Carnivores and vice-versa (e.g. Bear). So, the area of intersection denotes Omnivores.
  • All Cows are pure Herbivores.

Relation Type 8

One class belongs to the second class and the third class is partly related to these two.

For example, the classes of Males, Brothers and Engineers.
Venn diagrams It means that:

  • All Brothers are Males.
  • Some Males are Engineers and vice-versa.
  • Some Brothers are Engineers and vice-versa.

Relation Type 9

Two separate classes belong entirely to the third class.

For example, the classes of Elements, Copper and Gold.
Venn diagrams It means that:

  • Both Copper and Gold are Elements.
  • No Copper is Gold and vice-versa.

Relation Type 10

Two classes belong to the third class such that some items of each of these two classes are common too.

For example, the classes of Carnivores, Herbivores and Animals.
Venn diagrams It means that:

  • Some Carnivores are Herbivores and vice-versa.
  • Both Carnivores and Herbivores are Animals.
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Last updated on Nov 5, 2020

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