Syllogisms: Concept explained with examples

Syllogisms form an integral part of reasoning. Questions from this topic frequently appear in various MBA entrance exams like CAT, SNAP, IIFT, etc; Bank PO exams and other aptitude tests.

Syllogism is a form of reasoning in which a conclusion is drawn from two or three given propositions or statements. It uses deductive reasoning rather than inductive reasoning. You have to take the given statements to be true, even if they are at a variance from established facts.

Let us see an example of deductive reasoning.

Statements:
  1. All cats are dogs.
  2. All dogs are birds.
Conclusion – All cats are birds.

This conclusion is quite visible. But to solve complex problems we have some standard methods.

Method 1- Analytical Method

Following are the four major types of statements generally asked:

Sr. No. Type of statement Represented by the letter Example
1 Universal Positive A All boys are handsome
2 Universal Negative E No girl is clever
3 Particular Positive I Some rats are dogs
4 Particular Negative O Some ships are not planes

While deriving conclusions, following points should be kept in mind:

  • With two particular statements, no universal conclusion is possible.
  • With two positive statements, no negative conclusion is possible.
  • With two negative statements, no positive conclusion is possible.
  • With two particular statements, no conclusion is possible, except when an 'I' type of statement is given and then by reversing it, an 'I' type of conclusion is given.
Important points related to conclusions drawn from single statements.
  • A statement of type 'E' when reversed, gives a conclusion of type 'E & O'.
  • A statement of type 'A' when reversed, gives a conclusion of type 'I'.
  • A statement of type 'I' when reversed, gives a conclusion of type 'I'
  • A statement of type 'O' when reversed, does not give a conclusion of any type.
Method 2- Venn Diagrams

Another method of solving such type of questions is by drawing Venn diagram representing the statements. However, it is important that all possible Venn diagrams be drawn. If a conclusion can be deduced from all the possible solutions then that conclusion is true. If the conclusion can be concluded from one of the possible Venn diagram and not from the other possible Venn diagram then that conclusion is taken as false.

Suggested Reading :
Learn the basic concepts of Venn Diagrams.
Solved Examples

Example1:Which of the two conclusions can be concluded on the basis of given statements?

  • Statements:
  • Some parrots are scissors.
  • Some scissors are not combs.
  • Conclusions:
  • Some scissors are parrots.
  • Some combs are parrots.

Solution: Now, in this case, the possible conclusion is: Some scissors are parrots (I to I), as the universal principal no. 4 says, that with two particular statements only I to I is possible. Therefore, only 1 conclusion is possible. Nothing else is possible.

Example 2 : Which of the two conclusions can be concluded on the basis of given statements?

  • Statements:
  • All flowers are candles.
  • All lanterns are candles.
  • Conclusions:
  • Some flowers are lanterns.
  • Some candles are lanterns.

Solution:

Three possible diagrams are shown above for the given statements.
Conclusion I follows from last two possible solutions, but does not follow from the first possible solution. Therefore, this conclusion is false.
Conclusion II follows from all the three possible solutions.
Therefore, conclusion II is true.

Example 3: Which of the two conclusions can be concluded on the basis of given statements?

  • Statements:
  • All prisoners are men.
  • No man is educated.
  • Conclusions:
  • All prisoners are uneducated.
  • Some men are prisoners.

Solution: Two possible diagrams are shown below for the given statements.

Conclusion I follows from both the possibilities, so conclusion I is true.
Conclusion II also follows from both the possibilities, so conclusion II is also true. 
Therefore, both conclusions are true.

Example 4: Which of the two conclusions can be concluded on the basis of given statements?

  • Statements:
  • All sides are lengths.
  • No length is a breadth.
  • Conclusions:
  • All lengths are sides
  • No breadth is a side

Solution: Two possible diagrams are shown below for the given statements.

Conclusion I: False (conclusion follows from the second possibility but doesn't follow from the first possibility)
Conclusion II: True (conclusion follows from both the Venn diagram possibilities.)
Therefore, only conclusion II is true.

Test your understanding of the topic: Syllogisms now.
 

Previous Year CAT questions

To know the importance of this topic in various exams, take a look at some previous year CAT questions.

Question 1: The question has a set of four statements. Each statement has three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

  • Directions questions asked in the exam are based on two principles-
  • Citizens of Yes Islands speak only the truth. Citizens of Yes Islands are young people. Young people speak only the truth.
  • Citizens of Yes Islands speak only the truth. Some Yes Islands are in the Atlantic. Some citizens of Yes Islands are in the Atlantic
  • Citizens of Yes Islands speak only the truth. Some young people are citizens of Yes Islands. Some young people speak only the truth.
  • Some people speak only the truth. Some citizens of Yes Islands speak only the truth. Some people who speak only the truth are citizens of Yes Islands.
A) A only
B) B only
C) C only
D) D only

Solution: Option C
Only C is the correct answer choice. Statement A is invalid. We cannot conclude about 'all YP', but only about 'Some YP' (shaded portion) who are, incidentally, 'all CY'.

CYI = Citizens of Yes Islands

ST = People who speak only the truth

YP = Young people

Statement C is valid. The 'Some YP' who are CYI also are people who speak only the truth. (Shaded portion)

Statement D is invalid, because the 'some people' and the 'some CYI' need not have any relationship between them, just because both speak only the truth.

Question 2: The question has a set of four statements. Each statement has three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

  • Many singers are not writers. All poets are singers. Some poets are not writers
  • Giants climb beanstalks. Some chicken do not climb beanstalks. Some chicken are not giants
  • All explorers live in snowdrifts. Some penguins live in snowdrifts. Some penguins are explorers
  • Amar is taller than Akbar. Anthony is shorter than Amar. Akbar is shorter than Anthony.
A) A only
B) B only
C) B and C
D) D only

Solution: Option B

Statement A is invalid, as no definite relationship between P and W can be established.

Note: 'Many' is translated as 'Some' to convert the statement in standard form.

The 'Some S (shared portion)' are not w, but some other S could be W, as shown in the Venn diagram above.

Statement B is valid, as the 'Some C (shaded portion)' that do not climb beans stalks cannot be giants.

G = Giants

C = Chicken

CB = Creatures which climb beanstalks C is invalid, the 'Some penguins' that live in snowdrifts need not be explorers.

D is invalid, as Amar is the tallest among the three, but it is not clear how the heights of Akbar and Anthony are compared.

Note: This is not a 'Categorical' syllogism comprising statements, as such. All S is P, No S is P, Some S is P and Some S is not P. It is a 'relational' syllogism comprising relational statements that normally feature in analytical reasoning. Be alert: CAT examiner is in the habit of jumbling up questions to throw you off gear.

Question 3: Choose an option in which the last statement can be deduced logically from the preceding two. Example:

  • All cigarettes are hazardous to health.
  • Brand X is a cigarette
  • Brand X is hazardous to health
A) ABC
B) BCA
C) CBA
D) CAB

Solution: Option A) ABC is a valid option, where statement C can be concluded from statements A and B

Question 4: The question has a set of five statements. Each option has three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them

  • Ant eaters like ants.
  • Boys are ant-eaters
  • Balram is an ant-eater
  • Balram likes ants
  • Balram may eat ants
A) DCA
B) ADC
C) ABE
D) ACD

Solution: Option D

BI = Balram

AE = Ant-eaters

LA = Creatures who like ants

Anteaters like ants and Balram is an anteater.

Therefore, Balram likes ants.

  • DCA is invalid. Just because Balram likes ants and he is also and anteater, it does not logically follow that all anteaters like ants. It would, however, be valid to conclude that 'Some anteaters like ants'.
  • ADC is invalid, because if Balram lke ants, we cannot definitely conclude that Balram is an anteater, as evident from the Venn diagram.
  • ABC is invalid, because it has four terms:

Ant-eaters, creatures who like ants, boys and Balaram

Furthermore, E: 'Balram may eat ants' can never feature in a valid syllogism. A 'may’ statement implies 'may not' and is not always true. Hence, such a statement is of no use to a student of logic, who is concerned with the process of reasoning, arriving at a definite conclusion from definite information given in the premises..

Suggested Reading :
Learn How to find Maxima & Minima using Venn Diagrams
Key Learning
  • Syllogisms use deductive reasoning rather than inductive reasoning. You have to take the given statements to be true, even if they are at a variance from established facts.
  • If a conclusion follows from one of the possibility, but does not follow from another possibility, then that conclusion is regarded as false

You can also post in the comment section below, any query or explanation for any concept mentioned in the article.