Syllogism

Introduction

Definition

Syllogism has been defined as “A form of reasoning in which a conclusion is drawn from two given or assumed propositions”. It is deductive reasoning rather than inductive reasoning. It can be stated that an important part of the exam is Syllogism in reasoning.
Let us take two propositions as follows:

1. All men are old.
2. All old wear caps.

We can conclude on the basis of the above two statements that "All men wear caps"
However, the validity of the conclusion is important. Not all conclusions need to be valid. Only those two propositions which lead to a valid conclusion are relevant to our cause.
For Example

1. All tasks are pending.
2. Some books are pending.

The conclusion that "Some books are tasks" is invalid.

You might be facing some difficulties regarding which type of statement can lead to what type of conclusion. If you understand the rules given below and their proper use, you are likely to commit no mistakes.

Basics of Syllogistic Reasoning

"A class is defined to be the collection of all objects that have some characteristics in common". Classes can be related to each other in many ways. If every member of one class is also a member of a second class, then the first class is said to be included or contained in the second. If some but perhaps not all members of one class are also member of another, then the first class may be said to be contained partially in the second class. Of course, there are pairs of classes having no members in common, such as the class of all triangles and the class of all circles.

Now let us take 4 statements

1. All persons are kind.
2. No person is kind.
3. Some persons are kind
4. Some persons are not kind.

The first statement is about two classes and clearly defines that the first class is included in the second.
The second statement says that the first class is wholly excluded from the second.
The third statement says that at least one member of class 1 is also a member of class 2.
The fourth similarly implies that at least one person is not kind.
Note: it is important to understand the above four statements completely before proceeding further.

Universal Positive Statement

First of all universal means something which is applicable to all and positive means, this is of ‘yes’ format. Universal positive statement indicates something positive applicable to all the items in that category. This is represented by the letter ‘A’. These statements begin with All, Each and Every.
Some Examples are: All boys are sharp, All girls are cute, All Indians are kind.
Every computer is a fan. Each of the colleges is a school.
All these are ‘A’ type of statements, because they all are conveying universal positive meanings.

Universal Negative Statement

Again, in this case, the only difference from the last category is that, in this case, the statement conveys a negative meaning. It implies that it refers to that kind of statements, which are universal and giving a negative impression. These types of statements begin with No, None of the, Not a single etc. and are represented by the letter ‘E’. Some examples of these types of statements are:
No S is P. No person is intelligent. No Rita is Meena. No boy is smart.
None of the girls is busy. Not a single person is sleeping.

Particular Positive Statement

In this case, the statement given gives a positive impression but it covers only some items and not all. This type of statements begins with some, any, a few and are represented by the letter ‘I’.
Some examples of I type statements are:
Some lawyers are actors, some fruits are apples, few books are keys.
Some staplers are mobiles.

Particular Negative Statement

Here, the statement again covers only some items, but it gives a negative impression. These kinds of statements are represented by the letter ‘O’. Some examples of this are…

Some boys are not crazy, some files are not pencils, some m is not n,
Some Rohit are not Dhawan’s. Few vegetables are not green.

The definitions of the A, E, I, O statement are very important and the student must be able to immediately recognize the statement.
With these things in mind, given below is a list of all the four types of statements.

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Practice Questions:

Q1. Consider the following three statements:
1. Only students can participate in the race.
2. Some participants in the race are girls.
3. All girl participants in the race are invited for coaching.
Which one of the following conclusions can be drawn from the above statements?
(a) All participants in the race are invited for coaching.
(b) All students are invited for coaching.
(c) All participants in the race are students.
(d) None of the statements (a), (b) and (c) given above is correct.

Q2. Consider the following statements:
1. All machines consume energy
2. Electricity provides energy
3. Electrically operated machines are cheap to maintain
4. Electrically operated machines do not cause pollution.
Which one of the following inferences can be drawn from the above statements?
a) All machines are run by electric energy.
b) There is no form of energy other than electricity
c) Most machines are operated on electric energy.
d) Electrically operated machines are preferable to use.

Q3. Examine the following statements:
1. None but the rich ran afford air-travel.
2. Some of those who travel by air become sick
3. Some of those who become sick require treatment
Which one of the following conclusions can be drawn from the above statements?
a) All the rich persons travel by air.
b) Those who travel by air become sick
c) All the rich persons become sick.
d) All those who travel by air are rich

Q4. Examine the following statements:
1) I watch TV only if I am bored
2) I am never bored when I have my brother’s company.
3) Whenever I go to the theatre I take my brother along.
Which one of the following conclusions is valid in the context of the above statements?
a) If I am bored I watch TV
b) If I am bored, I seek my brother’s company.
c) If I am not with my brother, than i'll watch TV.
d) If I am not bored I do not watch TV.

Q5. Examine the following statements:
1. None but students are the members of the club.
2. Some members of the club are married.
3. All married persons are invited for dance.
Which one of the conclusions can be drawn from the above statements?
a) All students are invited for dance
b) All married students are invited for dance
c) All members of the club are married person
d) None of the above conclusions can be drawn

Q6. Consider the following statements:
1. All X-brand cars parked here are white.
2. Some of them have radial tyres
3. All X-brand cars manufactured after 1986 have radial tyres are parked here.
4. All cars are not X-brand.
Which one of the following conclusions can be drawn from the above statements?
a) Only white cars are parked here.
b) Some white X-brand cars with radial tyres are parked here.
c) Cars other than X-brand cannot have radial tyres.
d) Most of the X-brand cars are manufactured before 1986.

Q7. Consider the following statements:
1. All artists are whimsical.
2. Some artists are drug addicts.
3. Frustrated people are prone to become drug addicts.
From the above three statements it may be concluded that:
a) Artists are frustrated
b) Some drug addicts are whimsical
c) All frustrated people are drug addicts.
d) Whimsical people are generally frustrated

Q8. Examine the following statements:
1. Either A & B are of same age or A is older than B
2. Either C & D are of same age or D is older than C
3. B is older than C
Which of the following conclusions can be drawn from the above statements?
a. A is older than B
b. B and D are of the same age
c. D is older than C
d. A is older than C

Q9. Examine the following statements:
1. Only those who have a pair of binoculars can become the member of the birdwatcher's club.
2. Some members of the birdwatcher's club have cameras.
3. Those members who have cameras can take part in photo-contests.
Which of the following conclusions can be drawn from the above statements?
a) All those who have a pair of binoculars are members of the birdwatcher's club.
b) All members of the birdwatcher's club have a pair of binoculars.
c) All those who take part in photo-contests are members of the birdwatcher's club.
d) No conclusion can be drawn.

Q10. During the summer vacation Ankit went to a summer camp where he took part in hiking, swimming and boating. This summer, he is looking forward to a music camp where he hopes to sing, dance and learn to play the guitar.
Based on the above information four conclusions as given below, have been made. Which one of these logically follows from the information given above?
a) Ankit's parents want him to play guitar.
b) Ankit prefers music to outdoor activities.
c) Ankit goes to some type of camp every summer.
d) Ankit likes to sing and dance.

Q11. Statements: Some actors are singers. All the singers are dancers.
Conclusions:

• Some actors are dancers.
• No singer is actor.
  A. Only (1) conclusion follows
  B. Only (2) conclusion follows
  C. Either (1) or (2) follows
  D. Neither (1) nor (2) follows

Q12. Statements: All the harmoniums are instruments. All the instruments are flutes.
Conclusions:

• All the flutes are instruments.
• All the harmoniums are flutes.
  A. Only (1) conclusion follows
  B. Only (2) conclusion follows
  C. Either (1) or (2) follows
  D. Neither (1) nor (2) follows

Q13. Statements:

• Some mangoes are yellow.
• Some tixo are mangoes.
  Conclusions:

1. Some mangoes are green.
2. Tixo is yellow.

A. Only (1) conclusion follows
B. Only (2) conclusion follows
C. Either (1) or (2) follows
D. Neither (1) nor (2) follows

Q14. Statements:

• Some ants are parrots.
• All the parrots are apples.
  Conclusions:
• All the apples are parrots.
• Some ants are apples.
  A. Only (1) conclusion follows
  B. Only (2) conclusion follows
  C. Either (1) or (2) follows
  D. Neither (1) nor (2) follows

Q15.
Statements:

• Some papers are pens.
• All the pencils are pens.

Conclusions:

• Some pens are pencils.
• Some pens are papers.

A. Only (1) conclusion follows
B. Only (2) conclusion follows
C. Either (1) or (2) follows
D. Neither (1) nor (2) follows
E. Both (1) and (2) follow

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