Study Bindaas

Syllogisms Tricks with Examples:

Hi friends Syllogisms is one of the easy to win questions in reasoning, but we have seen so many aspirants are finding difficult in solving these questions. Usually Venn diagram method (Easy) is used to solve these but they will consume time in case of NO/Possibility conclusion cases. So here we are explaining the concept of Syllogism with some examples by using some simple rules.
First and foremost have a quick glance at the Main rules to solve Syllogism Problems…

All+All=All
All+No=No
All+Some=No Conclusion

Some+All=Some
Some+No= Some Not
Some+Some= No Conclusion

No +All = Some Not (Reversed)
No+Some=Some Not (Reversed)
No+No=No Conclusion
Some Not /Some Not Reversed +Anything = No Conclusion

If the conclusion is in “Possibility” case then these rules must be applied.

If All A are B then we can say - Some B are Not A is a Possibility
If Some B are Not A then we can say - All A are B is a Possibility
If Some A are B then we can say - All A are B is a Possibility All B are A is a Possibility

That is

All <=> Some Not Reversed
Some => All
NO Conclusion = Any Possibility is true

When it is implemented (In case of Conclusion from Single Statement)

All => Some that means if All A are B then Some B are A is true.
Some <=> Some that means if Some A are B then Some B are A is true.
No <=> No that means if No A is B then NO B is A is true

How to use these Syllogism Rules to solve questions?

In order to solve Syllogism there are two types:

Cross Cancellation
Vertical Cancellation

Let us see about Cross Cancellation with example:
Example 1:
Statements:

All Cows are Parrots
All Parrots are Birds
No Bird is Monkey

Conclusions:

No Parrot is Monkey
Some Cows being Monkey is Possibility

We know you might be able to solve it by using Venn diagram method that's good but this method won't help or a bit tough when it comes to No or possibility Conclusions

Here is explanation
Lets take 1st conclusion, we have to make relation between Parrot and Monkey so we will take statements 2 and 3.

This is called Cross Cancellation , We have cancelled Bird from Bird so we have left with (ALL+NO) rule, and that leads to No Parrot is Monkey So Conclusion I is TRUE.

In second statement we have Cow and Monkey so we will need to make relation between them. For this we need to take all 3 statements.

Syllogisms Three Statements Example Explanation

Now we have left with ((All+All)+NO) that is No Cow is Monkey . We don’t have any rule to convert this statement into Possibility so second conclusion is FALSE

I think we are clear with above explanation now see about Vertical Cancellation
Example 2:
Statements:

Some Mails are Messages
All Updates are Messages

Conclusion:

All Mails Being Update is a Possibility
No Update is Mail

Lets take Conclusion “All Mails Being Update is a Possibility” that means we have to make relation between Mails and Updates

This is called Vertical cancellation. In this case direction of adding first phrase will be reversed i.e In
Above example the conclusion will be All+Some = No Conclusion.

IF we get No Conclusion in case of Possibility then according to Rules in Possibility case will be definitely true. So Conclusion 1 follows and Conclusion 2nd Don’t.

So far we have seen how to deal with All, Some, Some Not and No now let us see about Some Not in reversed condition.

What is Some Not (Reversed)?
To explain this let’s take a Simple example

No A is B
All B is C

So the conclusion you get for this will be as follows
(No+All) A is C = (Some Not Reversed) A is C
Therefore
Some C are Not A.

Finally my advice is...
Use this only if there are No or Possibility conclusions by following the above rules else you can happily use Venn Diagram method (If you find this method useful though). Don't get more confused for easy topics by doing unnecessary faults.

Lastly feel free to ask us if you have any doubts....
Enjoy Reading

Update:
Hi guys recently I have found one rule and some terms that are asking in tests these days which I intend to share with you guys...

"No" statement can be converted into two types
1. Some Not
2. No (interchanging Subject and Predicate)

Confused???
Let me explain this with an Example
Suppose statement is given as No Professor is Student then this statement can be valid to take as
1. Some Professor are not Student
2. No Student is Professor

clear

Another update is now a days in exams they are mentioning None, Only, Almost etc instead of All, Some in both statements and conclusions so I'm listing the terms here.

All => Every, Each, Any, None, Not a single, Only
Remaining will be treated as follows
Some, Many, a few, Quite a few, Not many, Very little, Most of, Almost, Generally, Often, Frequently, Atleast