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 nonconclusion 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 mugup 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 11^{th} hour.
 United Nations hates negativity. (both Universal and particular)
 Pritish Nandy hates everybody.
 Twonegatives=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 mugup rules as well.
ConclusiveCombos  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!
Thanks
All the best!!!
very helpful!! Thank yu so much..:)
You are most welcome Vidya :)
Hi pallavi ji
Thanks for ur tips and tricks
and really they are helping a lot in solving syllogisms in short time.
can u plz explain me this ?
statements : all bags are chalks
all chalks are bottles
conclusion : 1.some bottles are bags
2. all bags are bottles
3. all bottles are bags
4. some chalks are not bags
answer for this question in rs agarwal book is con 1,2,4 follows
i know conclusion 1,2 follos but how come conclusion 4 follows?
plz clarify this
Statement 1 says “All bags are chalks”
hence, Some chalks are bags
hence, Some chalks are not bags.
This way conclusion 4 also follows
I hope it helped you.
Thanks
But what if Chalks and Bags are equal sets?
but maine to padha h ki positive statement k sath negative conclusion doesnt follow
answr 1 and 2 follws..not 3 and 4….some not ke cndtn jb aayege jb not kaa reltn exist hoga..so ur anwer is corect 1 and 2
thank u very much.
i understood it now
stmts : all trolleys are pulleys
some pulleys are chains
all chains are bells
con :
1.some bells are trolleys
2.no bell is trolley
3.some pulleys are bells
4.all chains are pulleys
i know tat con 3 follows
but in rs agarwal they gave either 1 or 2, and 3 follows
can u plz explain this tat how come con 1,2 follows?
Hi Janhvi,
U hav forget to chk either or pair…1 When both conclu. is worng and one positve and one negative and one must be particular then either or case applied. Hence Either 1 or 2 as well as 3rd follow.. chek original post at mrunal.org
janvi g simpil h .. ya to bells trolleys hongi ya nhi hongi… koi 3 chij to ho nhi sakti .. so either aya..
i hav a doubt ji
1.all goats r cows
some goats r lambs
conc1: all goats r lambs
conc2:some lambs r cows ANSWER ME ,A>B coversion must or not??and my book answer is CONC2 follows,but ur method shows NO CONC… plz reply???!
answer me pls……all r getting wrong ans.
SOME+SOME and ALL+SOME
very nice tips and tricks….
so much thanks……
All the pencils are inks.
Some inks are pencils.
wath is the solution of this question
No Conclusion
Because All + Some = No Conclusion
hi jahnavi:
therecan be two different cases
1st : some pulleys are chains include trolley
2nd : some pulleys are chain does not include trolley
so if 1st case is true then conclusion 1 follows and if 2nd case is true then conclusion 2 follows
in either case conclusion 3 follows and 4 doe snot
so either 1 or 2 and 3 follows
Please Give me a example of syllogism with this…
No + All = Some not reversed
No + Some = Some not reversed
Thank you
Please help me to solve this
1.All apartments are huts.
2. No hut is a building.
3 . All buildings are cottage
Conclusion.
*1 .No apartment is a cottage
*2 Some buildings being apartment is a possibility.
Conclusion..
*1Some cottages being apartment is a possibility.
*2. No cottage is hut.
Please explain.
Jahnavi Ji,
In this case we must go with venn diagram process
1.
A) ALL BIRDS ARE CATS
B) SOME CATS ARE CRAZY
C) SOME DOGS ARE BIRDS
D) BIRDS ARE CRAZY
2. Which of these FORM pair so that the conclusion can be derived from them?
1) AB 2) BC 3)CD 4)AD
First option..use t venn diagram u can find it
Hi Jahnavi, if you by venndiagram.
Then u can find ur answer.
if UP+PP gives no conclusion
then how all+some=some is possible
it should be all+some=no conlusion
plz rply…
THAT IS NOT ALL+SOME
THAT IS SOME +ALL =SOME
PP+UP=PP
most teachers are boys.some boys are students.answer is some students are boys.
can u explain me how
cz its some+some or particular +particular which leads to no conclusion
look at the sentence
some boys are students=PP
PP–>PP
hence
boys=A,students=B
A to B —>B to A
some students are boys
most teachers are boys –i think its a PP
so PP cannot mingle with PP that is PP–PP=no conclusion
so u can avoid that sentence and check with the conclusions
hope it helps u..
all bags are cakes .
all lamps are cakes.
conclu:some lamps are bags
no lamp is bag.
what will b the answer and how
all bags are cakes=UP
all lamps are cakes=UP
A—>B
C—>B
no conclusion can be drawn
all fishes are grey in color.some fishes are heavy should give no conclusion since its all+some but the answer is given all heavy fishes are grey in color…is it right???
all jungles are tigers.some tigers are horses.
conclusions:
some horses are jungle .
no horse is jungle
answer given is: Either a or b follows
is it right?n how?
thanks very helpful… :)
Thank you Sandy
THANKS FOR YOUR EASIEST WAYS IN DEALING WITH SYLLOGISM
Thanks Thomas..
I think this is one of the most important info for me.
And i’m glad reading your article. But should remark on some general things, The
web site style is perfect, the articles is really great : D.
Good job, cheers
If example is : All cats are dogs . All cows are dogs.
Answer is : No conclusion.
How to explain this on above rules ?
Statements: All pens are books
Some pencils are pens
Conclusions: 1. some books are pencils
2. Some pencils are books
3. All pens are pencils
4. None
A.) 1 B.) 2
C.) 3 D.) 4
Can someone help me with the above question. The answer says only conclusion B) is right. Whereas in my opinion A) and B) both follows….kindly help!
what exactly does some not reversed mean?
If some x are y then can we say that some x are not y?
sir plz explain how to solve probability case k
STATEMENT:
SOME APPLES ARE FRUIT
SOME FRUITS ARE SOUR
CONCLUSION:
SOME APPLES ARE SOUR
SOME SOURS ARE FRUIT
This article is good, however it needs some emphasis on the middle term distribution aspect. Article is incomplete.
Thanks this is really very helpful.
Thanks these rules are very important to solve problems.
hey guys help me with this and thank you for shortcuts
a. All ambulances are life savers.
b. No ambulances are bumper cars.
1.No life savers are bumper cars
2.No bumper cars are life savers
3.Some life savers are no bumper cars
4.None of the above
all+some=no conclusion but in wiki(http://en.wikipedia.org/wiki/Syllogism) it says this
All rabbits have fur. (MaP)
Some pets are rabbits. (SiM)
∴ Some pets have fur. (SiP)
WHAT IS THE DIFFERENCE BETWEEN WHEN AND ONLY WHEN AND IF AND ONLY IF