Syllogism

The syllogism is an integral part of all the aptitude questions papers. It falls under the category of logical reasoning. Over the years syllogisms have achieved an important place in the aptitude exams, due to its mystifying nature. It is advised to solve the question of the syllogism as the last question of attempt as it requires a lot of patience and logical level of analysis. Following is the list of exams where the questions of syllogisms are frequent.

List of exams:-

  1. CAPF
  2. Regional Rural Banks
  3. Bank Exams
  4. Staff Selection Commission
  5. SBI Exams
    1. SBI PO
    2. SBI Clerk
    3. SBI SO
  6. IBPS Exams
    1. IBPS PO
    2. IBPS Clerk
    3. IBPS Specialist Officer

Following is the list of topics of syllogisms

  1. Introduction to syllogisms
  2. Statements of syllogisms
  3. Application of Venn diagrams
  4. Logical deduction
  5. Steps to solve syllogism questions
  6. Solved examples

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.

To know more about Govt Exams, check at the linked article.

The questions which are asked in this section contain two or more statements and these statements are followed by two or more conclusions. One ha to find out which of these conclusions logically follow from the given statements. The statements have to be taken true even if they seem to be at variance from the commonly known facts.

There are many ways of solving questions of syllogisms. The most effective and efficient method of all is using a Venn diagram. On the basis of the given statements, one should draw all the possible diagrams and then arrive at the solution from each of these diagrams separately. Finally, the answer common to all the diagrams is taken as the correct one.

Statements of syllogisms

The questions of syllogisms of three main parts.

  1. Major premise
  2. Minor premise
  3. Conclusion

The major premise is a statement in general believed to be true by the author.

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.

Application of Venn diagrams

In order to identify whether the given conclusion is correct or not draw the Venn diagrams according to major and minor statements.

Cases of Venn diagram

The above represents the combination of major and minor statements in two different ways. In the first case, the statement “ All women are smart “ the Venn diagram of women is inside the Venn diagram of smart. Hence the major statement is true. And since Amanda is a woman the Venn diagram representing Amanda should be inside Woman. In the sceond case, the only difference is, the major statement “ All women are smart “ the Venn diagrams of Women and smart are overlapping with each other. Because that’s another possibility. Since Amanda is women it is represented inside it. Observing both the cases we can agree that the conclusion given “ Amanda is a smart “ is true from both the case.

Note: The conclusion should be true according to all the possible cases. One should draw all possible cases before arriving at the conclusion. Below the table that provides that correct combination of Venn diagrams of major and minor premises.

Important Bank/Govt Information:

Logical deduction

Major premise

Minor premise

Conclusion

Conclusion True/false

All dogs are cats.

All cats are bulls.

All bulls are dogs.

False(it’s true only according to 3rd case)

All dogs are cats.

All cats are bulls.

All dogs are bulls.

It’s true( In all the three cases)

Three different cases of Venn diagram

Steps to solve syllogism questions:

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

Ex: Man, doctor, pilot, etc.

  1. Draw a Venn diagram corresponding to each variable, a number of Venn diagrams is equal to the number of variables.
  2. Deduce the logical level by reading the statements and draw the corresponding Venn diagram
  3. Check the conclusions given by comparing it with the Venn diagram obtained
  4. Select the correct conclusion.

The following table gives the correct representation of Venn diagrams applying the above rules.

Variables

Number of variables

Best possible representation

Thief, Robber


2

Venn diagram of thief and robber

Women, Mothers, and Engineers.

3

Venn diagram of women , mothers and engineers

Bangalore, India, Asia, Karnatka.

4

Venn diagram of Asia, India, Karnataka , Bangalore.

Solved examples:

Type 1 questions of syllogisms

Instructions: 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

Solution:

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.

Example 1-Overlapping and non overlapping cases of Venn diagram

Instructions: Observe the following premises and select if the conclusion is

Correct/ Incorrect

Example 2:

Major premise: No pencil is cloth.

Minor premise: No sweaters are pencils.

The conclusion is: All sweaters are cloth

A. Correct

B. Incorrect

Solution:

Explanation:

In this case, as it can be seen there are three possible scenarios.

Since “ No pencil is cloth” The diagram of pencil and cloth do not have any overlapping and hence they are just touching each other( the diagram can also be represented by keeping them apart, but that will not affect the logical conclusion). According to the minor premise, since no sweaters are pencils the diagrams of sweaters and pencil do not overlap.

Case 1: If no sweaters are pencil, one possibility is there can be no sweater which is no cloth also.

Case 2: There can be a sweater which is also cloth. Hence a part of sweater and cloth overlap with each other.

Case 3; All clothes can be a sweater, as there is not any promise which says this combination is not possible.

The conclusion “all sweaters are cloths” is correct only according to 3rd case but not with respect to the 1st and 2nd case. Hence the conclusion is incorrect.

Example 2 -Non, partial and complete overlapping of Venn diagram - 1

Type 2 questions of syllogisms.

Observe the following premises and select the correct conclusion.

Example 3:

Major premise: All engineers are innovative.

Minor premise: All students are engineers.

Conclusions:

  1. All innovative are students
  2. All students are innovative
  3. No innovative are students
  4. No engineers are students

Solution:

Example 3- Venn diagrams

Explanation:

The first conclusion “ All innovative are students” is wrong according to case 1 and case 2. The sceond conclusion is correct in all three cases. Conclusion 3 and 4 are not correct according to all the three cases. Hence the correct answer is option B.

Example 4:

Major premise:No computers are televisions.

Minor premise:All radios are televisions.

Conclusions:

  1. All radios are computers
  2. No radios are computers
  3. All computers are radio
  4. None of the above

Example 4- Venn diagrams

Explanation:

The conclusion “ All radios are computers” is not true according to both the Venn diagrams. The second conclusion is true according to both the diagrams as both the Venn diagrams do not overlap with each other anywhere. The conclusion “ All computers are radio” is also wrong according to both the diagrams. Hence the correct answer is option B.

Type 3 questions of syllogisms.

Example 5:

Statements:

  1. All Stones are Hammers
  2. No Hammer is Ring
  3. Some rings are doors
  4. All doors are windows

Conclusions:

  1. Some hammers are stones
  2. Some windows are rings
  3. Only (1) conclusion follows
  4. Only (2) conclusion follows
  5. Either(1) or (2) follows
  6. Neither(1) nor (2) follows
  7. Both (1) and (2) follow

Solution:

Example 5- Venn diagrams

Explanation:

The first conclusion “Some hammers are stones” is not true according to case 5, where all the shammers are stones. The second conclusion” Some windows are rings “ is true in all the three cases. Hence the correct answer option is B.

Example 6:

Statements:

All cups are books.

All books are shirts.

Conclusions:

i. Some cups are not shirts.

ii. Some shirts are cups.

  1. Only (1) conclusion follows
  2. Only (2) conclusion follows
  3. Either(1) or (2) follows
  4. Neither(1) nor (2) follows
  5. Both (1) and (2) follow

Solution:

Example 6- Venn diagrams

Explanation:

Four combinations of Venn diagrams are possible according to the two premises. The first conclusion “some cups are not shirts” is not true in all the three cases, as all the cups are shirts in every case. The second conclusion “ some shorts are cups” is true only in the first three cases, whereas in the last case it’s not true(all the shirts are cups). Hence neither conclusion 1 nor 2 is correct. Hence the correct answer is option D.

Leave a Comment

Your email address will not be published. Required fields are marked *