Syllogism | Logical Reasoning for CLAT PDF Download

What is Syllogism?

The word syllogism is derived from the Greek word “syllogismos” which means “conclusion, inference”. Syllogisms are a logical argument of statements using deductive reasoning to arrive at a conclusion. The major contribution to the filed of syllogisms is attributed to Aristotle.

Statements of syllogisms

The questions of syllogisms of three main parts.

• Major premise
• Minor premise
• Conclusion
  The central premise is a statement in general, believed to be true by the author.
  
  Question for Syllogism

  Try yourself: Observe the following statements and select if the conclusion is

  Correct/ Incorrect

  Example 1:

  Major premise: All Actors are right-handed.

  Minor premise: All right-handed are Artists.

  The conclusion is: Some Artists are Actors.

  • A.

    correct
  • B.

    incorrect

  Explanation

  Case 1:

  The Venn diagram of actors is inside right-handed and which in turn is inside the Venn of artists. According to the diagram, the portion of the red Venn diagram overlapping with green indicates that some actors artist are actors. Hence the conclusion is correct according to this diagram, but can not be concluded as the final answer until the second case is checked.

  Case 2: Since all the Venn diagrams are overlapping with each other, according to the diagram all the artists are actors or all the actors are artists. Hence the conclusion is “ some artists are actors” is wrong. Since the conclusion is wrong according to the second Venn diagram. The correct answer will be option B incorrect.

  

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Example: All women are smart.

The minor premise is a specific example of the major premise.

Example: Amanda is a woman.

The conclusion is a specific statement which logically follows both major and minor statement.

Example: Amanda is smart.

Steps to solve syllogism questions:

1. Note the number of variables present in the given statements

Ex: Man, doctor, pilot, etc.

2. Draw a Venn diagram corresponding to each variable; several Venn diagrams is equal to the number of variables.

3. Deduce the logical level by reading the statements and draw the corresponding Venn diagram

4. Check the conclusions given by comparing it with the Venn diagram obtained

5. Select the correct conclusion.

Identify the type A, E, I, O: 

A ➜ Affirmative Positive

E ➜ Affirmative Negative

I ➜ Particular Positive

O ➜ Particular Negative

Understanding Syllogism with the help of Venn Diagram:

Different Types of Arguments

1. Affirmative Positive - A type 

Example: All ‘A’ are ‘B’.
From this statement, it can be inferred that:

• Some ‘A’ are ‘B’.
• Some ‘B’ are ‘A’ is a definite conclusion.

Note:  All ‘B’ are ‘A’ is a possibility but  it may not be true in all cases

2. Affirmative Negative - E Type 

Example: No ‘A’ are ‘B’.
Conclusions which can be drawn from the given statement are:

• Some ‘A’ are Not ‘B’. 
• No ‘B’ are ‘A’.  
• Some ‘B’ are not ‘A’.

3. Particular Positive - I Type 

Example: Some ‘A’ are 'B’
From the given statement, we can conclude: 

• Some ‘B’ are ‘A’. (i)
• However, All ‘A’ are ‘B’. (i) 
• All ‘B’ are ‘A’. (ii)
• Some ‘A’ are ‘B’. (iii)
• Some ‘A’ are not ‘B’ and Some ‘B’ are not ‘A’ is not a definite conclusion.

4. Particular Negative - O Type 

Example: Some ‘A’ are not ‘B’.
It cannot be explained with a diagram. Moreover, no logical conclusion can be drawn from the given statement.  There can be more than one possibilities in which this argument can be represented.
They are as under:

The shaded portion shows the A, which is not B.

Deriving Logical Conclusions When Various Types ofrguments are Given Together

1. All ‘A’ are ‘B’,  All ‘B’ are ‘C’    (A & A)                 
This argument is represented below:

 Conclusions:

• All ‘A’ are ‘C’, 
• Some ‘C’ are ‘A’,  
• Some ‘C’ are ‘B’,
• Some ‘A’ are ‘C’
• (All ‘C’ can be ‘A’, All ‘B’ can be ‘A’ but may not be defiantly true in all the cases.)

2. All ‘A’ are ‘B’, No ‘B’ are ‘C’  (A & E)
This argument is represented below:

• No ‘A’ is ‘C’.
• Some ‘A’ are not ‘C’. 
• Some ‘C’ are not ‘A’. 
• All ‘A’ are ‘B’.

3. Some ‘A’ are ‘B’, All ‘B’ are ‘C’ (I & A)

This argument can be represented by Figure 9 as well as figure 10.

Conclusions which are definitely true in both the cases:

• Some ‘A’ are ‘C’. 
• Some ‘C’ are ‘A’. 
• Some ‘B’ are ‘A’.

Note: All ‘A’ are ‘C’ , Some ‘A’ are not ‘C’ , Some ‘A’ are not ‘B’ and vice versa can be a possibility but may not be true in all the cases. The other possibility is as under.

4. Some ‘A’ are ‘B’, No ‘B’ are ‘C’ (I & E)   

This argument can be represented by Figure 11, 12 & 13.

Conclusions which are definitely true in all the possible cases:

• Some ‘A’ are not ‘C’. 
• Some ‘B’ are not ‘C’. 
• No ‘C’ is ‘B’. 
• Some ‘C’ are not ‘B’.

The shaded portion shows A which are not C.

Note: Any conclusion with ‘C’ as subject and ‘A’ as predicate is not a definite conclusion.

5. No ‘A’ are ‘B’, All ‘B’ are ‘C’ (E & A)

This argument can be represented by Figure 14, 15, & 16.

Conclusions which are definitely true in all the cases:

• Some ‘C’ are not ‘A’. 
• No ‘B’ is ‘A’. 
• Some ‘B’ are not ‘A’. 
• Some ‘A’ are not ‘B’.

The shaded portion shows C, which are not A.

Note: Any conclusion with ‘A’ as subject and ‘C’ as predicate is not a definite conclusion.

6. No ‘A’ are ‘B’, Some ‘B’ are ‘C’ (E & I)
This argument can be represented by Figure 17, 18 & 19.

Conclusions which are definitely possible in all the cases: 

• Some ‘C’ are not ‘A’. 
• Some ‘A’ are not ‘B’. 
• Some ‘B’ not ‘A.’ 

Note:  Any conclusion with ‘A’ as subject and ‘C’ as predicate is not a definite conclusion.