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SYLLOGISM

Syllogism is one of the important topics in competitive exam  . The Technique we will discuss here is one of the shortest and fastest way of solving Syllogism.

First things you need to know is few rules


Rules for alignment or conversion of statements are

A(All A are B)              →    I(Some B are A)  
E(No A is B)                →    E(No B is A)
I(Some A are B)          →    I(All B are A)
O(Some A are not B)   →    not convertible

this means if a you have got derived conclusion as All A are B but in it is given(in question) conclusion that some A are B or some B are A than you can say given conclusion follows 

Example: Statement: All Car are Bikes. 
                Conclusion : some Bikes are Car


So we can say conclusion follows 

In this blog we have discussed few easy examples to explain the concept but in exam you might face various types of questions so we suggest you to go through the Article in this link here  to learn the basic concept . If you follow the mentioned article and get accustomed with the cancellation methods explained here ..after practicing few Question sets you can solve without pen and paper...
              
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A(All A are B) + A(All B are C)                           →         A(All A are C)
A(All A are B) + E(No B is C)                             →         E(No A is C)
E(No A is B) + A(All B are C)                              →         O reverse(Some C are not A)
E(No A is B) + I(Some B are C)                          →         O reverse(Some C are not A)
I(Some A are B) + A(All B are C)                        →         I(Some A are C)
I(Some A are B) + E(No B is C)                          →         O(Some A are not C)
O reverse(Some B are not A) + A(All B are C)               →         O reverse(Some C are not A)

any other combination will result to No conclusion

for complete list you can check here here 

iF 

The methods are Vertical (L.H.S (Left hand side cancellation) R.H.S (right hand side cancellation)) and Cross Cancellation method ...

will be updated soon...

Left Hand Side LHS Cancellation - SYLLOGISM |Vertical Cancellation
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Lets take an example to understand this concept  

Example1) No Bike is Car. Some Bike are Buses

Soln.

No    Bike is Car 

Some Bike are Buses

In case of LHS Rule is Reverse alphabetical order i.e here it should be now, as in reverses alphabetical order 'S' comes first than 'N'

 Some(Buses) + No(Car) => O( Some Buses are not Car)

Example 2) Some Bike are Buses.  No Bike is Car

Some Bike are Buses

No    Bike is Car

So, Some (Buses)+ No(Bike) =>O( Some Buses are not Car)

Right hand side RHS  Cancellation - Syllogism |Vertical Cancellation
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Example 3) Some Buses are Bikes.  No Car is Bike

Some Buses are Bike 

No Car is Bike 

In case of RHS we will consider alphabetical order . 

No(Car) + Some(Bus) => O reverse (Some Buses are not car)

Example 4) No Car is Bike. Some Buses are Bikes.

No Car is Bike 

Some Buses are Bike 

No(Car) + Some(Bus) => O reverse (Some Buses are not car)

Cross Cancellation | Syllogism
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Example 5) Some officers are Politician.  All Politicians are Thieves. Some Thieves are Criminal.

Some  Officers are Politicians 
All       Politicians are Thieves 
Some Thieves are Criminal 

So Conclusion is Some + ALL  => Some and Some + Some => No Conclusion 

in details:

Some  Officers are Politicians 
All       Politicians are Thieves 
Some (Officers) + All (Thieves )=> Some officers are Thieves 
Some officers are Thieves
Some Thieves are Criminal

Some (Officers) + Some (Criminal) => No conclusion    (As I + I => No conclusion)


Example 4:) All Politicians are Thieves . Some officers are Politician. 
in this type of case :                        

Some  Officers   are Politicians 
All     Politicians are Thieves 

So conclusion is: Some (Officers) + All (Thieves )=> Some officers are Thieves 

SYLLOGISM POSSIBILITY:
this is the most searched syllogism related contents ..we have explained here with few rules ..if you follow the article http://www.affairscloud.com/syllogism-made-easy/ than it will be vary easy for you to solve any kind of Questions.



So lets understand what is possibility- if some one says' ALL A are B ' than we can say : some A  are B - possible , Some B are A - possible  ..so in case of various statement (A, I ,O , E) what are the possible conclusion we can find out through following rules

If Given (in question) conclusion is in Possibility than you can apply following rules to check whether the given conclusion follows or not ...

* If your derived conclusion or statement is:

1)  if 'All A are B'  then -> Some B are not A is a possibility
2)  If 'some B are not A' then we can say: All  A are B is a possibility 
3)  If 'Some A are B ' then we can say  : All A are B is a possibility or All B are A is a possibility .
4) In case of No conclusion all possibility cases are true 5) We do not have any rules to convert 'No' into any possibilities.

few points
1. in case of LHS and RHS cancellation if the statemets are ALL+ ALL => No conclusion 
but in case of cross cancellation it follows the rule i.e A+ A => A

2. Universal Positive or negative : All, Every , any none, not a single, only etc.
3. Universal negative : Some, many, a few, quite a few, not many, very little, most of, almost, generally, often, frequently, etc.

You need to classify the statement in ALL/ Some/Some Not /Not form only  to use rule.

Syllogism | Either or Case in Syllogism

Conditions:

1. If both Conclusions are incorrect after applying rules

                                               AND

2. If One conclusion is positive an other is negative

Syllogism Possibilities with Examples | Syllogism

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