Venn Diagram Questions: Tips & Tricks

Logical Venn Diagram

What exactly is the Venn diagram?

These diagrams were given by John Venn. To put it simply, these diagrams show all possible logical relations between a number of elements.
In a typical Venn diagram, usually, there’s a use of geometrical figures like Circles, Triangles, Squares & Rectangles.

A basic Venn diagram has data represented in ‘Circles’.

1. In a country three persons A, B and C live. They are three different persons. This information can be represented as:

Here, we can see that A, B and C are different elements so they’ve represented by different circles.

2. if we were to represent information in which two elements are intermingled while the third one is different we’ll do that a bit differently.

For example, Hindu, Indian, Parrot. Now, logically we know that Some Hindus are Indian (as some Hindu might be living abroad and be Australian or any other country’s citizen) and also, no Parrot is Hindu(as animals have no religion) also no Parrot is Indian (as no animal has ethnicity). This information of Hindu, Indian, Parrot can be represented as follows:

Here, the shaded area shows those Hindus who are Indians at the same time. Parrot is represented in a different circle.

3. Suppose, we need to convey this: Dog, Animal, Cow.
Now we know that all dogs are animals (clearly no dog is human) so the circle of ‘dog’ will have to be completely surrounded by a circle of the animal through the circle of animal can have some spare space aside from dog as the dog isn’t the only animal. Similarly, all ‘cows’ are animals so the circle of ‘cow’ will have to be completely surrounded by the circle of animal through the circle of animal can have some spare space aside from cow as the cow isn’t the only animal. This information can be represented as:

Here, we can see that ‘Animal’ has been represented by a big circle that encompasses the circles for both ‘cow’ and ‘dog. Notice, the circle for ‘animal’ has some spare space as this can contain other types of animals because ‘cow’ and ‘dog’ aren’t the only types of animal.

Types of questions asked in Competition Exam:
Let’s have a look at the type of questions asked in exam. There are basically two types of questions:
1) Finding relationship: To solve these kinds of questions, we need to have a strong grip on common relationships that exist in the world around us. Like to define the relationship between Catholics & Christian we need to know that Catholics are the type of Christians hence we can easily conclude that all Catholics are Christian but some Christians will not be Catholics as they will be the other type of Christians. This information can be represented as:

A typical question might look like this: Dean, Painter, Singer.
We live in a diverse world where people can be multi-talented also people possess just one talent so this info can be represented by 7 categories of people:
a) Who are only Dean

b) Who are only Painter

c) Who are only Singer

d) Who are both Dean & Painter

e) Who are both Painter & Singer

f) Who are both Singer & Dean

g) Who are all Dean, Painter & Singer?
This information can be represented by Venn-diagram as follow: (for reader’s convenience, the different regions have been labelled as named above but in exams, questions haven't marked this way)

2) Finding the exact region: These are the reverse version of the questions discussed above. Here, the diagram with labelled image is given and we’ve to identify the region specifically asked the question.
For example, an image like below will be given:

Circle S stands for households having a scooter, Circle T stands for households having a TV set,
Circle W stands for households having a Washing Machine, Circle C stands for households having a car.
Find household having both TV set, Car and Washing Machine but not scooter. (Question ends)

Now, if we look closely we can see that four distinct items have been, these 4 distinct items can be seen as:

Now, there are places where only ‘Circle S and Circle T’ meet, such place can be represented in the figure below with ‘orange’ colour, similarly, following colours have been used to represent different regions:
1) Green = Only (T, W and S) 2) Yellow = Only (T and W) 3) Purple = Only (W and C) 4) Blue = Only (S, W and C) 5) Baby Pink = Only (S and T) 6) White = Only (S, T and C) 7) Light brown = Only (T, W and C) 8) Red = All S,T, W and C.

Note: You don’t have to make such colorful representation in the exam. It’s been only colourized to help you visualized the different regions with specific labels.
Now, we have to find the household with TV, Washing machine, car but not scooter.
We know that TV = Circle T, Washing Machine = Circle W, Car = Circle C, Scooter = Circle S
So, we have to find where Circle T, W and C meet but not S.
We can clearly see that such region is represented by light brown region which was marked as ‘7’ in the original question figure.
The similar question can be given which represents different elements using different figures like the rectangle, triangle etc. as shown below:

Here, Circle represents college Professors, the triangle represents Surgeons and Chemist are shown by the rectangle.
Find the area where Surgeons who are Chemists but not Professors are represented.
To find the area representing only Surgeons and Chemists, we need to look for the where ONLY Triangle(=Surgeons) and Rectangle(=Chemist) meet and no sign of Circle(=professor).
Clearly, such area is shown by region marked as Z only (and not Y because that would include Circle also).