Syllogism 69

Chapter

15 Syllogism

INTRODUCTION All the sentences mentioned above give

a relation between subject and predicate.
Syllogism is a Greek word that does mean
Here, it is clear from the sentences that a
‘inference’ or ‘deduction’. The problems subject is the part of a sentence
of syllogism are based on two parts : something is said about, while a predicate
1. Proposition / Propositions is the term in a sentence which is related
2. Conclusion / Conclusions drawn from to the subject.
given proposition/ propositions Now, let us define the proposition :
A proposition is a sentence that makes a
PROPOSITION statement giving a relation between two
Just consider the sentences given below: terms. It has three parts :
(a) The subject
(b) The predicate
(i) “All lions are pigs ”
(c) The relation between subject and
predicate
Subject Predicate
CATEGORICAL PROPOSITION
Let us see the sentences given below :
(ii) “No cat is rat ” “All M are P”
“No M are P”
Subject Predicate “Some M are P”
“Some M are not P”
What we notice in all above-Mentioned
(iii) “Some girls are beautiful ” sentences that they are condition free.
These type of sentences are called
Categorical Propositions. In other
Subject Predicate
words a categorical proposition has no
condition attached with it and it makes
direct assertion. It is different from non-
(iv) “Some kites are not birds ” categorical proposition which is in the
format
Subject Predicate “If M then P”

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 70 Syllogism
TYPES OF CATEGORICAL PROPOSITION:
Categorical proposition

Universal Particular

Positive Negative Positive Negative

All M are P No M are P Some M are P Some M are not P

(A type) (E type) (I type) (O type)

Therefore, it is clear, that universal

propositions either completely include P
the subject (A type) or completely
exclude it (E type). On the other hand, Some M are P (I type):
particular propositions either only partly Either:
include the subject (I type) or only partly
exclude the subject (O type).
Now, we can summarise the four types M P
of propositions to be used while solving
the problems of syllogism :
Some M are P
Format Type
[Some M are not P]
All M are P A
Or :
No M are P E
Some M are P I M
Some M are not P O
P
q Shortcut Approach
All M are P (A type): Some M are P
[All P are M]
P Some M are not P (O type):
and M, P Either:
M
[Possibility] M P
No M are P (E type):
Some M are not P
M [Some M are P]
Or:

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Syllogism 71
EXAMPLE
P No one (student) is studious.
M [No student is studious]
(i) A negative sen tence with a
Some M are not P particular person as its subject is
[All P are M] E type propoistion.

HIDDEN PROPOSITIONS He does not deserve Bharat Ratna

(A) A type: Subject Predicate

Apart from ‘all’ it starts with every, Amitabh Bacchan is not a great actor.
each and any.
Subject Predicate
EXAMPLE (ii) Sentences in following formats are
Every girl is beautiful. E type :
[All girls are beautiful.] “No student except
(i) A positive sen tence with a definite exception
particular person as its subject is
A type. Reena has failed”

He should be amended Bharat Ratna “Is there any truth left in the
world”
[No truth is left in the world.]
Subject Predicate (C) I type:

Amitabh Bacchan is a great actor. Apart from some it also starts with
words such as often, frequently,
almost, generally, mostly, a few,
Subject Predicate most etc.
(ii) A sentence in with a definite
EXAMPLE
exception is A type :
(i) Almost all the girls are beautiful.
definite exception [Some girls are beautiful].
(ii) Most of the garments are
“All girls except Reeta are healthy.” handmade.
[Some of the garments are
handmade].
(B) E type:
It is clear from the above examples
Apart from ‘no’ this type of that negative sentences begining
propositions starts from ‘no one’, with words like ‘few’, ‘rarely’,
‘seldom’, etc. (Also ‘hardly’,
‘none’, ‘not a single’ etc. ‘scarcely’, ‘little’ etc.) are to be
reduced to I type.

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 72 Syllogism
Just see the other formates given below Also, see the following formates :

Not a definite exception as name of No definite exception as name of

girls are not given. girls are not given.

All girls except a few are beautiful.

No girls except three are beautiful.
[Some girls are beautiful]
[Some girls are not beautiful.]
Not a definite exception as name of
girls are not given. No definite exception as name of
women are not given.

All girls except 5 have passed

No women except a few are housewife.
[Some girls have passed]
Therefore, a positive proposition with Therefore, a negative proposition with
an indefinite exception is reduced to I
an indefinite exception, is reduced to O
type.
type.
(D) O type :
Apart from “Some ....... not’ this EXCLUSIVE PROPOSITIONS
type of statements start with words
Such propositions start with ‘only’,
like ‘all’, ‘every’, ‘any’, ‘each’, etc.
‘alone’, ‘none else but’, ‘none but’ etc.
EXAMPLE and they can be reduced to either A or E
(i) All girls are not beautiful. or I format.
[Some girls are not beautiful] EXAMPLE
(ii) Poor are usually not healthy.
[Some poor are not healthy] Only graduates are Probationary
Now, it is clear from the above mentioned Officers.
examples that negative propositions with Þ No graduate is Probationary
words such as ‘almost’, ‘frequently’, Officer (E type)
‘most’, ‘mostly’, ‘a few’, generally, etc. Þ All Probationary Officers are
ar e to be reduced to th e O–type graduates. (A type)
propositions. Þ Some graduates are Probationary
Again, positive propositions starting Officers (I type)
with words like ‘few’, ‘scarcely’, ‘rarely’, General format of sentences given in the
‘little’, ‘seldom’ etc. are said to be O– examinations :
type. All M are P (A type)
EXAMPLE No M are P (E type)
Seldom are women jealous. Some M are P (I type)
[Some women are not jealous] Some M are not P (O type)

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Syllogism 73
Note : General format given above are After conversion it becomes
frequently asked formats in the
Subject Predicate
examinations. But students must be
ready for other hidden formates of A,
E, I and O types of propositions as “Some P are M ” (I type)
problems in hidden formates can also
be given in question papers. Therefore, I gets converted into I.
(iv) Conversion of O type :
CONVERSION OF
O type of proposition can’t be
PROPOSITIONS converted.
Before solving the problems of syllogism Note : In each conversion, subject
it is must to know the conversion rules of becomes predicate and predicate
all A, E, O, and I types of propositions : becomes subject.
(i) Conversion of A type : In fact, conversion is an immediate
inference that is drawn from a single
Subject Predicate proposition while inference drawn from
two propositions are called mediate
“All M are P ” (A type) inference.
After conversion it becomes. q Shortcut Approach
Subject Predicate Table of conversion :
Type of Ge t conve rte d into
“Some P are M ” (I type) proposition

Therefore, it is clear that A type of A I

propositions get converted into I type. E E
(ii) Conversion of E type : I I
Subject Predicate O Never get converted
Rule to draw conclusion :
“No M are P ”(E type) After knowing con version of
propositions, we must learn the rules
After conversion it becomes to draw conclusions. In problems of
Subject Predicate syllogism, conclusions are drawn either
from single propositions or from two
“ No P are M ” (E type) proposition or from both. But a
conclusion from single proposition is
Therefore, E gets converted into E. just a conversion of that proposition
(iii) Conversion of I type : while to get conclusion from two
propositions a certain table is used that
tells us what type of conclusion (in form
Subject Predicate
of proposition) we get out of two
propositions. To understand it, let us
“Some M are P ” (I type) see the following conclusion table :

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74 Syllogism
Conclusion Table
I Proposition II Proposition Conclusion
A A A
A E E
E A (O)R
E I (O)R
I A I
I E O
Note : EXAMPLE
(a) Apart from above 6 pairs of Statements :
propositions, no other pair will
give any conclusion. I. No pen is chair..
(b) The conclusion drawn out of two
propositions is itself a proposition II. Some tables are pen .
and its subject is the subject of
the Ist statement while its EXAMPLE
predicate is the predicate of the
Statements :
2nd statement. The common term
get disappeared. I. Some women are men .
(c) (O) R does mean that the
conclusion is O type but is in II. No men is chair..
reverse order. In this case, the
subject of the inference or In all the above mentioned example, we
conclusion is the predicate of the notice that in two statements of every
2nd proposition and the predicate example, there is a common term. In
of the conclusion is the subject of example 1 the word ‘girl’ is common; in
the Ist sentence or statement. example 2 the word ‘pen’ is common
(d) The conclusion table gives while in example 3 the word ‘men’ is
correct conclusions or inference common.
if and only if the two propositions
Now, the aligning of the two statements
are aligned properly.
(propositions) does mean that the pair
WHAT IS ALIGNING ? of statements must be written in such a
way that the common term is the
Let us see the following examples :
predicate of the 1st sentence and the
EXAMPLE subject of the 2nd.
Statements : Just think over the following examples :
Statements :
I. All girls are beautiful.
I. Some girls are cute .
II. Some girls are Indian. II. All cute are tall.

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Syllogism 75
Here, the common term cute is the METHODS:
predicate of the I statement and subject (1) By Analytical Method
of the 2nd statement. Therefore, the two (2) By Venn Diagram
statements (I & II) are properly aligned. (1) Analytical method :
But see another example. This method has two main steps:
Statements : (a) Aligning the pair of sentences.
I. Some bats are chairs. (b) Using conclusion table to
draw conclusion.
II. Some cats are bats .
EXAMPLE Statements :
Here, the sentences are not aligned as
the predicate of the 1st statement is not I. All rats are cats.
the subject of the 2nd. II. All rats are men.
Then how to align it ? In such type of When aligned it takes the form as
cases we change the order of sentences. I. Some cats are rats [I type]
In another words we put I sentence in
place of II and II in place of I : II. All rats are men [A type]
II. Some cats are bats . Now we use the conclusion table
given in this chapter that says
I. Some bats are chairs. I + A = I type of conclusion.
Therefore, as per the requirement and Therefore, the drawn conclusion
nature of the sentence the alignment is must be
done. “Some cats are men”
(i) only by changing the order It is clear that the conclusion drawn
of sentences. “Some cats are men” is a mediate
or inference as it is the result of two
(ii) only by converting of the propositions. But in actual problem
sentences. immediate inferences are also given in
or conclusion part and that format is given
below :
(iii) By changing the order of the
statements and then EXAMPLE : Statements:
converting on e of the I. All rats are cats.
sentences. II. All rats are men.
IEA Rule Conclusion:
(i) Some cats are men.
Alignment must be done in IEA order. It (ii) Some men are cats.
does mean that if the two statements are (iii) Some rats are cats.
I & E then the conversion must be done (iv) Some cats are rats.
for I and for E & I it will be done for E. (v) Some rats are men.
After discussing all the minute things (vi) Some men are rats.
about this chapter, now we have come Here, all the options are correct.
at the position of solving the problems conclusion (i) follows because it is the
of syllogism. mediate inference of statements I & II.

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 76 Syllogism
Conclusion (ii) is the conversion of METHOD TO SOLVE
conclusion (i) conclusion (iii) is the (a) 1st step is sketching all possible
immediate inference (conversion) of pictorial representation for the
statement I while conclusion (iv) is the statements separately.
conversion of conclusion (iii). (b) 2nd step is combining possible
Conclusion (v) is the immediate inference pairs of these representations of
(conversion) of statement II while all the statements into one.
conclusion (vi) is the conversion of (c) 3rd and final step is making
conclusion (v). interpretation of this combined
Further, in some problems figure.
complementary pairs are also seen in th Conclusions are true if they are
e conclusion part in the forms of sentence supported by all the combined
figures in 2nd step.
given below:
(a) (i) Some cats are rats. EXAMPLE
(ii) Some cats are not rats I - O pair
Statements :
(b) (i) All cats are rats.
(ii) Some cats are not rats. A- O pair A. All chairs are books.
(c) (i) Some cats are rats. B. All books are ties.
(ii) No cats are rats. I- E pair Conclusions :
Apart from I - O, A - O and I - E pair the I. Some ties are books.
two sentences must have some subject II. Some ties are chairs.
and predicates as are the above 1st Step :
mentioned pairs. for these pairs we write
the form 'Either (i) or (ii) follows.
METHOD TO SOLVE b c t b
(a) First step is aligning the
sentences.
(b) Second step is using conclusion 1A 1B
table.
(c) Third step is checking immediate
inferences.
(d) Fourth step is checking through c, b b, t
the conversion of immediate
inferences & immediate inferences.
(e) First step is checking the 2A
2B
complementary pairs. Here, 1A and 2A are representations for
(2) Venn diagram method for solving statement A while 1B and 2B are
problems : representations for statement B. In these
Students will have to adopt three representations
steps to solve the syllogism b = books
problems through Venn diagram c = chairs
method : t = ties

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Syllogism 77
2nd step : POSSIBILITY
Let us combine all the possible pairs of
this pictorial representations : Possibility is a concept of inconsistency
for an event which is not yet verified but
if true would explain certain facts or
b c t phenomena.
Generally, the meaning of possibility is
probability, viz. possibility exists where
(1A + 1B) nothing is certain between the objects.
In general language determination of
possibility exist easily in that condition
b c t when between two objects have no
certainty or the truth facts accordingly.
Let's understand below table in which
(1A + 2B) possibility exists where no definite
relation occurs between the objects and
t c, b definite or proper relation between the
objects eliminate existance of any
possibility. In simple way given
condition eliminates the possibility and
(2A + 1B)
improper condition favours the
possibility. Here, we can go through with
c, b t an example which will also clear the term
possibility.
Condition Possibility
(2A + 2B) Given facts cannot be determined
3rd step :
When we interpret the pictures in step Imaginary facts can be determined
II, we find that all the pictures support
EXAMPLE
both the conclusions. Therefore,
conclusion I : Statements Some boxes are trees
“Some ties are books” and Some trees are hens.
conclusion II. Conclusions
“Some ties are chairs” I. Some boxes being hens is a
both are true. possibility
Note : In the Venn diagram method, II. All trees being hens is a
any conclusion given with any possibility
problem will be true if and only if it is
supported by all the combined
pictorial representations through 2nd Boxes Trees
step. If any pictorial representation
contradicts the given conclusion, it Hens
will be put in the category of incorrect Hens
or wrong conclusion.

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 78 Syllogism
In Conclusion I, before deciding the possibility between boxes and hens, we
must notice the relation between both, we find that there is no relation between
boxes and hens, so possibility favours the condition and the conclusion I is true
for possibility and in Conclusion II we must notice the relation between trees
and hens. We find that both have some type of relation between them so the
possibility of ‘All between trees and hens is true. Hence, both the Conclusions
I and II follow.
q Shortcut Approach

Desired
Given Exclusive Proposition Possibility
Proposition
All All ´
Some Some ´
No No ´
No Some not ´
Some All ü
No proper relation Some All ü

Note: Improper relation between two objects favours the possibility (In above
example Conclusion I)

SPECIAL CASES OF EXCLUSIVE PROPOSITION

Meaningful
If the statement is of Conversion Illustration
Conversion
Much, more, many, Some Most A are B. Some A and B.
very, A few X are Y. Some X or Y.
a few, most, almost
Atleast Some Atleast some A are B. Some A and B.

Definitely No use Some A are definitely B. Some A are B.

Some X are definitely not Y. Some X are not Y.
Only Only A are B. All B are A.
1% to 99% Some 38% A are B. Some A are B.
98% X are Y. Some X are Y.

ebooks Reference Page No.

Practice Exercises with Hints & Solutions – P-108-117

Chapter Test – C-29- 30

Past Solved Papers

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