Syllogism Reasoning Tips

Syllogism

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 Possiblity
• 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:

Ex: Statements:

1. All Cows are Parrots
2. All Parrots are Birds
3. No Bird is Monkey

Conclusions:

1. No Parrot is Monkey
2. 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

Let's take the first conclusion, we have to make a 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 a relation between them. For this we need to take all 3 statements.

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

ex: Statements

1. Some Mails are Messages
2. All Updates are Messages

Conclusion:

1. All Mails Being Update is a Possibility
2. No Update is Mail

Let's 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

1. No A is B
2. 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, 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.

Also, remember:

"No" statement can be converted into two types

1. Some not
2. No (interchanging Subject and predicate)

let's 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

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, at least.

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