         # Syllogism : An Introduction to Venn Diagrams In this article we are sharing the important concepts of syllogism and give you an introduction to venn diagrams which is the best way to solve syllogism questions usually asked in the Reasoning Sections of Bank Exams or any other competitive exams. To solve syllogism questions in the minimum possible time it is very much necessary to understand the basics of venn diagrams. By publishing this article we are starting a series on syllogism questions with solutions from basic to advance level, so stay connected with this website for further articles on the same topic.

What is Syllogism ?

Let us first understand the meaning and definition of Syllogism and how syllogism questions are being asked in competitive exams. Syllogism is a topic of verbal reasoning or logical reasoning and it is frequently asked in various competitive examinations. These types of questions contains two or more statements and these statements are followed by some conclusions. You have to find which conclusion follows logically from the given statements.

An Introduction to Venn Diagrams

The best method of solving Syllogism questions is through Venn Diagrams. There are four categories in which the relationships between Venn Diagrams can be made as per the statements given in the syllogism problems. Let us look in detail each category one by one.

Case 1.) All A are B

This statement means that “A is the subset of set B“. Here the whole circle representing A lies within the circle representing B as illustrated in the figure shown below.

The conclusions we can make from this statement may also include Some B are A or Some A are B.

Note : The statement ‘All A are B’ is different from ‘All B are A’

Case 2.) No A are B

This statement means that two sets A and B can never overlap each other. Here in this case the circle representing A will not intersect with the circle representing B. It is same as saying ‘No B are A‘.

On the other hand, this statement can also be written as ‘All A are not B‘. To understand it with the help of an example, lets say if the statement is ‘All Indians are not Ministers’ that means no Indian is a Minister.

Case 3.) Some A are B

This means that some part of the circle represented by A is within the circle represented by B. There is atleast one element that is both in set A as well as in set B. In short, some elements are only in set A, some elements are only in set B and some elements are in common, meaning that they are in both set A and set B.

From this statement we cannot infer that Some A are not B. For example, if the statement is ‘Some Indians are supporters of Rahul Gandhi’ that doesn’t mean that Some Indians are not supporters of Rahul Gandhi.

The statement ‘Some A are B‘ can also be represented as shown in the figure given below as they are symmetrical to each other.

(i) Some A are B also indicates that All A are B.

(ii) Some A are B also indicates that All B are A.

Note : The statement ‘Some A are B’ is same as the statement ‘Some B are A’.

Case 4.) Some A are not B

This statement means that some portion of circle A has no intersection with circle B or in other words there is at least one element in Set A that is not in Set B. It can be represented as shown in the figure given below.

The highlighted portion in the above diagram indicates that this area in Set A have no connection with Set B. But the fact which is required to be remembered is that we cannot infer this statement as Some A are B and it can be represented as shown below.

Note : This statement Some A are not B is different from Some B are not A.

## Important Points To Remember

1.  The ‘At least’ statement : Whenever ‘At least’ is used in the statements of syllogism it is considered similar to as ‘Some‘ statements.
For example : Statement – All directors are talented
Here the conclusion can be ‘Atleast some directors are talented’ or ‘Some directors are talented’.

2. The ‘Some not’ statement : Whenever ‘Some not’ is used in statements it’s considered opposite to ‘All type’ statements. Let’s take an example to understand it more clearly.

Statement :
Some Singers are Cricketers.
No Cricketer is a Writer.
Some Writer are Singers.

Here the Venn diagram for the above statements can be made as shown below.

The conclusion of given in the question was ‘Some Singers are not Cricketers’ then this conclusion will definitely be true. As in the above figure the shaded portion shows that some singers are not cricketers and in statement also it is given that no cricketer is a writer. So this conclusion will follow.

3. The Complementary Pairs : Either and or cases only takes place in complementary pairs. For example if the conclusion given are as follows.

(i) Some A are B
(ii) No A are B

Then from this conclusions it can be understood that if both the conclusions does not follow then any one of them will definitely be true and other one will be false simultaneously. Hence it is represented by option either (i) or (ii). These types of pairs are called complementary pairs.

Note : The fact which is also necessary to be remembered is that ‘All A are B’ and ‘Some A are not B’ are also complementary pairs. Let us understand this with the help of an example.

Statement :
All A are B
Some B are C

Conclusion :
(i) All C are A
(ii) Some C are not A

Here the Venn diagram of of the given statements can be made as shown above and as said the answer for this question will be Either (i) or (ii) follows.

That’s all in this article, hope you find it worthy and helpful. This is just an introduction article, we will be publishing more such articles on Syllogism with solved examples. In case if you had any doubt or feedback then please feel free to comment below. Keep sharing and Happy learning.

Thank You !! 