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6
Syllogism
Exam
Importance
Exam
Importance
CAT
Very Important
IBPS/Bank PO
Very Important
XAT
Very Important
BANK Clerk
Very Important
IIFT
Very Important
SSC
Very Important
SNAP
Very Important
CSAT
Very Important
NMAT
Very Important
Other Govt Exams
Very Important
Other Aptitude Test
Very Important
Introduction
Syllogism is one of the very important chapters for any aptitude test exam. In these types of questions premise
has generally two statements on the basis of which a deduction has to be made for conclusion. And then that
conclusion we have to select from the given options
2 We may have a case where from the given premise no conclusion can be drawn
There are two methods to solve these types of questions:(i)
Venn Diagram
(ii) Rules of deduction.
Now we will see how to derive conclusion from the given premise from these two methods but before that let’s have
a look at the different components of the premise and for that take two example of premise
All Rats are Hats……………….. (i)
All Hats are Pats……………….. (ii)
(i)
The premises normally start with qualifiers or quantifiers, e.g. the word All, No, some and Some – Not. The
word “All” has its synonyms as – Every, Any, Each, whereas the word “Some” can also be replaced by Many,
Few, A little, Most of, Much of, More, etc.
(ii) A premise consists of a subject and a predicate wherein the first term [e.g. “Rats” in statement (i)] is the
3 subject and the second term [e.g. “Hats” in statement (i)] the predicate. Similarly, in statement (ii), ‘Hats” is
called the subject and “Pats” is the predicate.
(iii) The word that occurs in both the premises is known as the ‘middle term’ (in this example since “Hats” is in
both the premise hence it is called middle term).
(iv) The “conclusion” of the premise middle term should not appear and conclusion should consist of the other two
words (“Rats” and “Pats” in the above example) and the.
The premises can be divided into 2 types (Based on qualifier)
(A) Universal statements [ if the qualifier used in the premise is “All”, “Every”, “Any”, “Each”]
(B) Particular statements [if the qualifier used in the premise is “Some”, Many, Few, A little, Most of,
Much of, More, etc]
The premises can be divided into 2 types (Based on type of statement)
(A) Positive (affirmative) statements [ if premise has no negation]
(B) Negative statements [If premise has a negative term like “not” or “no]
The combination of the two different categories of classifications leads to four different premises as given in Table
below.
Universal/ Particular
Affirmative/ Negative
“All”, “Every”, “Any”,
“Each”
Universal
Affirmative
“No” , “Not” “None”
Universal
Negative
Some, Many
Particular
Affirmative
Some not, Many not
Particular
Negative
The subject or the predicate can be either distributed or not distributed in the given premise.
The subject and the predicate are either distributed (indicated as yes) or not distributed (indicated as no) depending
on what kind of a statement it is. Table below shows the distribution pattern of the subject and the predicate.
Universal affirmative
Universal negative
Example
Subject
Predicate
“All”, “Every”, “Any”,
“Each”
Yes
No
“No” , “Not” “None”
Yes
Yes
Some, Many
No
No
Some not, Many not
No
Yes
Particular affirmative
Particular negative
Please note that:
(i)
Subject is distributed only in Universal statements.
(ii) Predicate is distributed in Negative statement.
RULES FOR DEDUCTIONS
1.
Every deduction should contain three and only three distinct terms.
2.
The middle term must be distributed at least once in the premises.
3.
If one premise is negative, then the conclusion must be negative.
4.
If one premise is particular, then the conclusion must be particular.
5.
If both the premises are negative, no conclusion can be drawn.
6.
If both the premises are particular, no conclusion can be drawn.
7.
No term can be distributed in the conclusion, if it is not distributed in the premises.
Now let’s take few examples to understand thisExample – 1) Find the conclusion of
4 (i)
All Rats are Pats
(ii) All Pats are Cats
Solution : Now look at the minute details of each premise(i)
Here the first statement starts with “All” which is Universal affirmative hence it is a universal affirmative
statement, and the subject (Rats) is distributed but the predicate (Pats) is not distributed.
(ii) The second statement is also Universal affirmative, the subject Pats is distributed and the predicate Cats is
not distributed.
(iii) Here the middle term is Pats as it occurs in both the premises.
(iv) Middle term is Pats is distributed once in the premises (In this example Premise ii) hence it satisfies Rule [2]
hence we can find a conclusion.
(v) Conclusion will have two terms and these terms are “Rats” and “Cats”
(vi) As “Rats” is distributed in the 1st premises and “Cats” is not distributed,
(vii) In final conclusion “Rats” is distributed but “Cats” is not distributed.
Conclusion: All Rats are Cats
Note of Caution: The conclusion cannot be All Cats are Rats as in this case we have distributed the
Venn diagram approach:(i)
All Rats are Pats: Can be represented as-
Pats
Rats
(ii) All Pats are Cats: Can be represented asPats
Cats
Overall conclusion is:
Cats
Pats
Rats
Hence final conclusion is all rats are cats.
Example –2) Find the conclusion of
(i) All Rats are Pats (ii) Some Rats are Cats
Solution: Now look at the minute details of each premise(i)
Here the first statement starts with “All” which is Universal affirmative hence it is a universal affirmative
statement, and the subject (Rats) is distributed but the predicate (Pats) is not distributed.
(ii) Here the 2ndstatement starts with “Some” which is Particular affirmative hence it is a Particular affirmative
statement, and the subject (Rats) is not distributed and the predicate (Pats) is not distributed.
5 (iii) Here the middle term is Rats as it occurs in both the premises.
(iv) Middle term is Rats is distributed once in the premises (In this example Premise i) hence it satisfies Rule [2]
hence we can find a conclusion.
(v) Conclusion will have two terms and these terms are “Pats” and “Cats”
(vi) In premise neither “Pats” nor “Cats” are distributed; so in conclusion “they should not be distributed.
Conclusion: Some Pats are Cats or some Cats are Pats
Venn diagram approach
(i)
All Rats are Pats: Can be represented as-
Pats
Rats
Rats
(ii) Some Rats are Cats: Can be represented asCats
6 Overall conclusion is:
Pats
Rats
Cats
Pats
Rats
Cats
Or
Hence final conclusion is Some Pats are Cats or some Cats are Pats.
Example – 3) Find the conclusion of
(i) All Rats are Pats (ii) No Pats are Cats
Solution: Now look at the minute details of each premise(i)
Here the first statement starts with “All” which is Universal affirmative hence it is a universal affirmative
statement, and the subject (Rats) is distributed but the predicate (Pats) is not distributed.
(ii) Here the 2ndstatement starts with “No” which is Universal negative hence both subject (Rats) and the
predicate (Pats) is distributed.
(iii) Here the middle term is Pats as it occurs in both the premises.
(iv) Middle term is Pats is distributed once in the premises (In this example Premise ii) hence it satisfies Rule [2]
hence we can find a conclusion.
(v) Conclusion will have two terms and these terms are “Rats” and “Cats”
(vi) Since one of the premises is negative hence conclusion must be negative.
(vii) In premise both “Rats” and “Cats” is distributed, so in final conclusion they should be distributed.
Conclusion: No Rats are cats or No Cats are Rats