Syllogisms

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 arecows.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

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

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)

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

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)

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)

Given Statement	Valid conversions	Type
Some Cats are Dogs	Some dogs are cats	Particular Positive (PP)

Type	Valid Conversion
Universal Positive (UP)	Only PP
Universal Negative (UN)	PN or UN
Particular Positive (PP)	Only PP
Particular Negative (PN)	Not possible.

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

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)

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.

Based on “xyz” and “not”, we classify the statements as following

Please remember following words. Whenever they come, you classify the statement accordingly.

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

CONVERSION:

Ok, so how to convert the statements?

Universal Positive (UP)

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)

It means UN can be converted into PN or UN.

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

Chapter 1  

STEP 3: NO CONCLUSION COMBOS

Here are the non-conclusion combos when two question statements are in following format.

^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 11^th 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

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.

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.