Venn Diagram


Reasoning is one of the most scoring subjects of all other competitive exams and one of the easiest chapter in this section is from “Venn Diagram”. Around 1-4 questions are covered from this topic and if the candidate is able to apply his thinking ability properly, he can easily score well in these questions.

LearnFrenzy provides you lots of fully solved "Venn Diagram" Questions and Answers with explanation.

What exactly is Venn-diagram?

1. These diagrams were given by John Venn. To put simply, these diagrams show all possible logical relationship between a numbers of elements.

2. In a typical Venn-diagram, usually there’s a use of geometrical figures like Circles, Triangles, Squares & Rectangles.

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

MIND IT !

The main aim of this section is to test your ability about the relation between some items of a group by diagrams. In these questions some figures of circles and some words are given. You have to choose a figure which represents the given words.


TIPS on cracking Reasoning Questions on Venn Diagrams


Tip #1: Start working from the outermost Venn diagram and gradually move inwards

Question: Which of the following diagrams indicates the best relation between Women, Mothers and Engineers?

venn-diagrams-logical-reasoning-tips---venn-diagrams


Solution:

Some women are mothers and some are engineers. All mothers are women, and some mothers are engineers. However, not all engineers are women. So, the answer is A.

Question: In an organization of pollution control board, engineers are represented by a circle, legal experts by a square and environmentalist by a triangle. Who is most represented in the board as shown in the following figure?

(a)   Environmentalists with Legal background

(b)   Legal Experts

(c)   Engineers with legal background

(d)   Environmentalists with engineering background

Solution:

venn-diagrams-logical-reasoning-tips---venn-diagrams

We have to assume that the shape with the largest area is the most represented. Among the given options, D (i.e.) Environmentalists with Engineering background has the largest area. Thus, the correct answer is D.


Tip #2: Reduce the question as the overlapping of different portions of the Venn diagram

In the following figure Upper Square represents the persons who know English, triangle those who know Marathi, Lower Square to those who know Telugu and circle those who know Hindi. In the different regions of the diagram, the counts are given.

Question: How many persons can speak English and Hindi both the languages only?

Solution:

The people who can speak English and Hindi is represented by the portion of intersection of the circle and the upper square only. The no. here is 5. So 5 people can speak Hindi and English both.

venn-diagrams-logical-reasoning-tips---venn-diagrams

Question: How many persons can speak all languages?

Solution:

The people speaking all languages is represented by the portion of the Venn diagram that has all the figures overlapping. Since there is no such area where all the figures are overlapping, it means that no person can speak all the languages.


Tip #3: The portion outside a figure represents the complement of the quantity inside it

In the following diagram rectangle represents men, Triangle represents educated, Circle represents urban and square represents government employees.

Question: How many men are educated but not urban?

(a)  9

(b)  5

(c)  4

(d)  11

Solution:

venn-diagrams-logical-reasoning-tips---venn-diagrams

Educated but non-urban men is represented by the portion of the triangle that overlaps with the rectangle but not the circle. Thus, 11 men are educated but not urban. The correct answer is D.

Question: Which one of the following represents a woman who is urban as well as government employee?

(a)  7

(b)  13

(c)  10

(d)  6

Solution:

Since the rectangle represents men, the portions of the other shapes that do not overlap with the rectangle represent women. The portion of the circle that overlaps with the square but not with the rectangle represents urban women who are government employees. Thus the answer is 10, i.e., C.


Some critical examples are given below:

Example 1:

If all the words are of different groups, then they will be shown by the diagram as given below.

Dog, Cow, Horse

             

All these three are animals but of different groups, there is no relation between them. Hence they will be represented by three different circles.


Example 2:

If the first word is related to second word and second word is related to third word. Then they will be shown by diagram as given below.

Unit, Tens, Hundreds

                 

Ten units together make one Tens or in one tens, whole unit is available and ten tens together make one hundreds.


Example 3:

If two different items are completly related to third item, they will be shown as below.

Pen, Pencil, Stationery

               


Example 4:

If there is some relation between two items and these two items are completely related to a third item they will be shown as given below.

Women, Sisters, Mothers

             

Some sisters may be mothers and vice-versa. Similarly some mothers may not be sisters and vice-versa. But all the sisters and all the mothers belong to women group.


Example 5:

Two items are related to a third item to some extent but not completely and first two items totally different.

Students, Boys, Girls

               

The boys and girls are different items while some boys may be students. Similarly among girls some may be students.


Example 6:

All the three items are related to one another but to some extent not completely.

Boys, Students, Athletes

                   

Some boys may be students and vice-versa. Similarly some boys may be athletes and vice-versa. Some students may be athletes and vice-versa.


Example 7:

Two items are related to each other completely and third item is entirely different from first two.

Lions, Carnivorous, Cows

               

All the lions are carnivorous but no cow is lion or carnivorous.


Example 8:

First item is completely related to second and third item is partially related to first and second item.

Dogs, Animals, Flesh-eaters

             

All the dogs are belonging to animals but some dogs are flesh eater but not all.


Example 9:

First item is partially related to second but third is entirely different from the first two.

Dogs, Flesh-eaters, Cows

      

Some dogs are flesh-eaters but not all while any dog or any flesh-eater cannot be cow.