IBPS/SBI PO BANKING STUDY MATERIAL ON SYLLOGISM BY ANALYTICAL METHOD
WHAT IS SYLLOGISM?
A syllogism is a kind of
logical argument in which one proposition (the conclusion) is inferred from two
or more others (the premises).
example:
Premise 1: All women are mothers.
Premise 2: All mothers are caring.
Conclusion: All women are caring.
All of us, who have given or are
preparing for any kind of entrance exam like CAT, SSC, MAT, XAT, SCAT
and others, have come across syllogisms. Venn diagrams are used to solve
syllogisms and are considered the standard way. But Alas! our exams’ time limit
does not provide us with the time enough to draw the diagram, label and shade
it and draw the conclusion out of it!
Then!! What to do?
Well there is not much to worry.
Here are some basic tips, tricks and step by step method which will help you to
solve a syllogism or at least make it somewhat easier.
- Shortcut rules (if Venn Diagrams are confusing you) between Statement 1 and Statement 2 in that order
All + All = All
All + No = No
All + Some = No Conclusion
Some + All = Some
Some + Some = No Conclusion
Some + No = Some Not
No + No = No Conclusion
No + All = Some not reversed
No + Some = Some not reversed
2. You can cancel out common terms
in two statements given, then on the remaining terms apply the syllogisms rules
and solve. E.g. Some dogs are goats. All goats are cows.out “goats”
which leaves us with Some dogs are…all are cows. Important words remaining
are SOME and ALL in that order. SOME + ALL = SOME, hence conclusion
is SOME dogs are cows.
3. Avoid using common knowledge as
Syllogisms questions usually state unnatural statements.
4. Remember some implications
All <=> Some, e.g. All A are B
also implies Some A are B (being a subset) and Some B are A
Some <=> Some, e.g. Some A are
B also implies Some B are A
No<=> No, e.g. No A are B also
implies No B are A
STEP 1: CLASSIFICATION OF
STATEMENTS:
In syllogism, each statement usually
has following format:
“xyz subject is/are (not)
predicate.”
For example,
Xyz
|
Subject
|
Is/are (+/-not)
|
Predicate
|
All
|
Cats
|
Are
|
Dogs
|
Some
|
Pigs
|
Are not
|
birds
|
Based on “xyz” and “not”, we
classify the statements as following
Statement
|
Type
|
Codename
|
1. All cats are dogs
|
Universal Positive
|
UP
|
2. Some dogs are birds
|
Particular Positive
|
PP
|
3. No bird is a pig
|
Universal Negative
|
UN
|
4. Some pigs are not birds.
|
Particular Negative
|
PN
|
Please remember following words.
Whenever they come, you classify the statement accordingly.
All, every, any, none, not a
single, only etc.
|
Universal (positive or negative)
|
Some, many, a few, quite a few,
not many, very little, most of, almost, generally, often, frequently, etc.
|
Particular (positive or negative)
|
STEP 2: STANDARD FORMAT:
CONVERSION(important: priority order for conversion is PP>UN>UP.)
Basically, a syllogism(we consider 2
premise syllogism here) should have the following basic form:
1. A—>B
2. B—>C
If it is not, then it needs to be
converted to the above format.
NOTE:
Question statements must have ONLY
three terms. (A, B and C).
In the exam, if they give you two
question statements with four terms then your time is saved! Just tick the
answer “no conclusion can be drawn”.
For example
Question statements
|
Answer
|
1. All cats are Dogs
2. Some birds are pigs
|
No conclusion can be drawn.
Because it has four terms (cats, dogs, birds, pigs)
A–>B
C–>D
|
CONVERSION:
Ok, so how to convert the
statements?
Universal
Positive (UP)
Given Statement
|
Valid conversions
|
Type
|
Given Statement: All Cats are Dogs
|
Some Cats are dogs
|
Particular Positive (PP)
|
Some dogs are cats
|
Particular Positive (PP)
|
It means UP can be converted into PP.
Please note: if the statement is
“Only Dogs are cats”, then better convert it into “All cats are dogs”. (Only A
is B –> All B are A)
Universal
Negative (UN)
Given Statement
|
Valid conversions
|
Type
|
Given Statement: No Cats are Dogs
|
Some dogs are not cats
|
Particular Negative (PN)
|
No dogs are cats
|
Universal Negative (UN)
|
It means UN can be converted into PN
or UN.
Particular
Positive (PP)
Given Statement
|
Valid conversions
|
Type
|
Some Cats are Dogs
|
Some dogs are cats
|
Particular Positive (PP)
|
It means PP can be converted into PP
only.
Particular
Negative(PN)
Example: Some Cats are not Dogs. In
Particular negative statements (PN), no conversion can be made.
To sum up the conversion rules
Type
|
Valid Conversion
|
Universal Positive (UP)
|
Only PP
|
Universal Negative (UN)
|
PN or UN
|
Particular Positive (PP)
|
Only PP
|
Particular Negative (PN)
|
Not possible.
|
STEP 3: NO CONCLUSION COMBOS
Here are the non-conclusion combos
when two question statements are in following format.
First statement (A to B)
|
Second statement (B to C)
|
Answer
|
Universal Positive (UP)
|
Particular Positive (PP)
|
No conclusion
|
Particular Negative (PN)
|
No conclusion
|
|
Universal Negative (UN)
|
Universal Negative (UN)
|
No conclusion
|
Particular Negative (PN)
|
No conclusion
|
|
Particular Positive (PP)
|
Particular Positive (PP)
|
No conclusion
|
Particular Negative (PN)
|
No conclusion
|
|
Particular Negative (PN)
|
Any other (UP, UN, PP, PN)
|
No conclusion
|
^does it look difficult?
Not really. Let’s condense this
table into mug-up rules.
- UP’s politicians hate giving particular statements (both positive and negative). E.g. they do not reveal their clear position on FDI in retail until the 11th hour.
- United Nations hates negativity. (both Universal and particular)
- Pritish Nandy hates everybody.
- Two-negatives=no conclusion. (although implicit in 2+3)
- Two particulars=no conclusion. (although implicit in 1+3)
STEP 4: CONCLUSIVE COMBOS
First statement (A to B)
|
Second statement (B to C)
|
Conclusion
|
Universal Positive (UP)
|
Universal Positive (UP)
|
Universal Positive (UP) (A to C)
|
Universal Negative (UN)
|
Universal Negative (UN) (A to C)
|
|
Universal Negative (UN)
|
Universal positive (UP)
|
Particular Negative (PN). (C to
A)
|
Particular Positive (PP)
|
||
Particular Positive (PP)
|
Universal Positive (UP)
|
Particular Positive (PP) (A to C)
|
Universal Negative (UN)
|
Particular Negative (PN) (A to C)
|
As you can see from above table,
The answer statement is usually in
the format of A to C. with exception when first question statement is Universal
Negative (UN).
Let’s condense this table into
mug-up rules as well.
Conclusive-Combos
|
In your head, visualize
|
|
If Uttar Pradesh meets Uttar
Pradesh, then its size doesn’t increase.
|
|
If Uttar Pradesh meets United
Nations then its size increases and it becomes United Nations.
|
|
United Nations Secretary Ban Ki
Moon is in very positive mood. But he meets another positive person, and his
attitude is totally reversed- he becomes particularly negative!
(reversed =C to A)
|
|
When Mr.PP observes the universe
via NASA telescope, his mood becomes positive or negative depending on the
mood of universe.
|
Following the above mentioned 4
STEPS and remembering some tips and tricks, you will be able to solve
syllogisms in an easy and less time consuming way.
Hit like if you found the post
useful… Hope it helps you!
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