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.
  1. 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.
  1. 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.
  2. United Nations hates negativity. (both Universal and particular)
  3. Pritish Nandy hates everybody.
  4. Two-negatives=no conclusion. (although implicit in 2+3)
  5. 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
  1. UP+UP=UP
If Uttar Pradesh meets Uttar Pradesh, then its size doesn’t increase.
  1. UP+UN=UN
If Uttar Pradesh meets United Nations then its size increases and it becomes United Nations.
  1. UN+ (UP/PP)=PN
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)
  1. PP+ (UP/UN)=PP/PN
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.


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