[Reasoning] Syllogism (All Cats are Dogs): Method, approach, techniques, shortcuts explained for IBPS, SSC, CSAT and CAT

Aptitude573 Comments

  1. Introduction to Syllogism
  2. Basics
  3. Subject vs Predicate
  4. Classification of statement
  5. Standard format: conversion
  6. No conclusion Combos
  7. Conclusive-Combos
  8. DemoQ: Crazy men and Women
  9. DemoQ: Intelligent Poets and singers
  10. CAT-level
  11. Special Conversions
  12. Complimentary pairs
  13. Tricky Situations: Priority order
  14. Tricky Situations: 1-Statement Conclusion
  15. Summary

Introduction to Syllogism

There are two main types of Syllogism question

2-Statements3-Statements
Question Statement:
I. All cats are dogs
II. All dogs are birdsConclusion:
I. Some cats are birds
II. Some birds are cats.
Question Statement
A. All cats are dogs
B. some pigs are cats
C. no dogs are birdsConclusion
I. some cats are dogs
II. no birds are cats
III. some pigs are birds
IV. some pigs are not birds
  • 2 Statement Syllogism questions are usually found in IBPS (Bank) and SSC exams.
  • UPSC CSAT 2012 exam had quite a few questions on 3 Statement Syllogism.
  • In CAT exams, they ask 2 Statement Syllogism but they pack 3-4 such “2-statement” syllogism questions inside one question to make it very time-consuming process.
  • In this article, you will learn how to solve the 2 Statement syllogism questions.
  • 3 Statement syllogism syllogism is explained in separate article (CLICK ME). (They’re mere an extension of the concepts explained in this article, so first master the 2-statement technique here.)

There are three methods to solve 2-statement Syllogism questions.

  1. Venn Diagram
  • In the exam, Have to think of all possible “Venn-Diagram” situation and draw them to check every statement.= time consuming in the exam hall.
  1. AEIO (analytical Method)
  • Have to mugup some rules, and spend some hours @home to master the “AEIO” conversion in your head. But once done, it is easy as a walk in the park.
  1. Distribution of terms (Tick method)
  • Usually taught in CAT coaching classes and study material.
  • Technique is very fast but It excludes the concept of “Conversion” and “Complementary cases”, hence sometimes makes it difficult to solve non-CAT questions.

The technique explained in this article, is a modified version of AEIO method combined with the Tick Method. Let’s call it U.P.-U.N. method.

Basics

Subject vs Predicate

Consider this question statement
1. All cats are dogs
2. Some dogs are birds
3. No bird is a pig
4. Some pigs are not birds.
In all such statements, first-term is called subject and second is called predicate.
It doesn’t matter what word is given: Table, Chair, Raja, Kalmadi, Kanimozhi or Madhu Koda – first term is subject and second term is predicate.
Let’s relook at those question statements

SubjectPredicate
1. All cats are dogsCatsDogs
2. Some dogs are birdsDogsBirds
3. No bird is a pigBirdPig
4. Some pigs are not birds.PigsBirds

I hope the Subject vs. Predicate is clear now. Let’s move to second thing

Classification of statement

In syllogism, each statement usually has following format
“xyz subject is/are (not) predicate.”

For example,

XyzSubjectIs/are (+/-not)Predicate
AllCatsAreDogs
SomePigsAre notbirds

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

StatementTypeCodename
1. All cats are dogsUniversal PositiveUP
2. Some dogs are birdsParticular PositivePP
3. No bird is a pigUniversal NegativeUN
4. Some pigs are not birds.Particular NegativePN

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, freqently, etc.Particular (positive or negative)

Standard format: conversion

The standard 2-statement syllogism question format is following:
1. (xyz) “A” is/are (+/- not) “B”
2. (xyz) “B” is/are (+/- not) “C”
So basically it is
1. A—>B
2. B—>C
(read as “A to B then B to C”)
What does this tell us?
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 statementsAnswer
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

Anyways back to the topic,
The standard format for question statements is:

1. A—>B
2. B—>C
1. First term—>Middle Term
2. Middle Term—>Third term

But if the given question statements are not given in this format, then we must convert them into above format. Otherwise we cannot proceed with answer. For example

Given question statements are
1. A—>B
2. C—>B
This must be converted into
1. A—>B
2. B—>C
Given question statements are
1. B—>A
2. B—>C
This must be converted into
1. A—>B
2. B—>C

Ok, so how to convert the statements?

Universal Positive (UP)

Given StatementValid conversionsType
Given Statement: All Cats are DogsSome Cats are dogsParticular Positive (PP)
Some dogs are catsParticular 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 StatementValid conversionsType
Given Statement: No Cats are DogsSome dogs are not catsParticular Negative (PN)
No dogs are catsUniversal Negative (UN)

It means UN can be converted into PN or UN.

Particular Positive (PP)

Given StatementValid conversionsType
Some Cats are DogsSome dogs are catsParticular Positive (PP)

It means PP can be converted into PP only.

Particular Negative

Example: Some Cats are not Dogs. In Particular negative statements (PN), no conversion can be made.
So PN=can’t convert.
To sum up the conversion rules

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

Please note:
In some lower level exams, sometimes they directly ask about conversion. For example
Q. What can be concluded from the given statement: “Some Politicians are honest men.”
Answer choices

  1. Some Honest men are not Politicians.
  2. All Honest men are not politician
  3. Some Honest men are politicians.
  4. None of Above.

(Please donot read further, without solving above question.)

Solution

well, the given statement “Some Politicians are honest men.” is a particular positive statement (PP).
Hence according to our table, it can be converted into PP only. Therefore

Given answer choiceThought process
  1. Some Honest men are not Politicians.
Particular negative (PN), hence eliminate.
  1. No Honest men are politicians.
Universal Negative, hence eliminate
  1. Some Honest men are politicians.
PP hence this is correct answer.
  1. None of Above.
–not applicable because C is the correct answer.

In case you are wondering,
Q. Some politicians are honest men.
In above case, can’t the answer be “A”: Some honest men are not politicians?
Well, if you go by Venn Diagram method, it’ll lead to two cases hence it is “doubtful”.

Case #1

Data
Subject (Politicians)
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Raja
  4. Kalmadi
Predicate (Honest Men)
  1. Sardar Patel
  2. Lal Bahadur Shastri

In above situation, can you say “Some honest men are not politicians”?
Well you can’t say that. Because both Honest men (Sardar and Shastri) are in politician set.

Case #2

Data
Subject (Politicians)
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Raja
  4. Kalmadi
Predicate (Honest Men)
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Bhagat Singh
  4. ChandraSekhar Azad
  • In above situation, can you say “Some honest men are not politicians”?
  • Yes you can. Because two Honest men (Bhagat Singh and Azad) are not in politician set.
  • The point is, whenever “two cases” are possible, you cannot ‘safely’ conclude one statement.

Hence, if the statement is

  • Some “A” are “B”–> it doesn’t mean Some “B” are not “A”.
  • The only valid conclusion in above case is :Some “B” are “A”.

Therefore Particular Positive (PP) statement can be converted into Particular Positive (PP) statement only.
Similarly

Type of StatementValid ConversionPath
Universal Positive (UP)All cats(A) are dogs (B)Only PPSome Cats (A) are dogs. (B)Some dogs (B) are cats. (A)A to BB to A
Universal Negative (UN)No Cats(A) are dogs (B)PN :Some Dogs (B) are not Cats (A).B to A
UN: No Dogs (B) are cats. (A)
Particular Positive (PP)Some cats (A) are dogs (B)Only PP: Some dogs (B) are cats(A)B to A
Particular Negative (PN)Not possible.

Anyways back to the topic, what are we discussing?

  1. Topic of discussion is: How to solve 2 statement syllogism question
  2. Subject vs predicate
  3. Type of statements (UP, UN, PP, PN)
  4. Standard format and conversion.

The standard question format is
A–>B
B–>C
If the given question doesn’t have statements in ^above standard format, then we must convert them into standard format. Only then we can proceed further.
So far, We constructed our shortcut table on how to convert the statements. Now

let’s try some examples

Question statementsConversion?
1. All Cats are dogs(B)
2. Some dogs(B) are not pigs.
Already in standard format (A to B and then B to C)
hence no need to convert.
1. Some dogs(B) are not pigs.
2. All Cats are dogs(B)
No need to convert any statement.
Just exchange the position of first and second statement.
1. All Cats are dogs(B)
2. Some dogs(B) are not pigs.
1. All Cats are dogs (B)
2. All pigs are dogs(B)
Have to convert, because not in standard format.1.All cats(A) are dogs(B)
2.Some dogs(B) are pigs(C). (Rule UP-> only PP)

Now coming to the heart of the matter: how to solve the (stupid) 2 statement syllogism question?

No conclusion Combos

Here are the non-conclusion 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 mug-up rules.

  1. UP’s politicians hate giving particular statements (both positive and negative). E.g. they donot reveal their clear position on FDI in retail until the 11th 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)

Please note: in ^above situations definite conclusion is impossible. However, sometimes two answer choices are still possible “either a or b”.
That concept is called “Complimentary pairs”. We’ll learn about it at the bottom of this article.
For the moment, let’s not complicate the matters with complimentary pairs.
Ok back to topic, when you face a “Two-statement syllogism question”? you’ll follow these steps:

  1. first, make sure it contains only three terms (ABC) (else no conclusion.)
  2. Make sure question statements are in standard format (A to B then B to C). If not in standard format, then re-arrange.
  3. Classify the question statements. (UP, UN, PP, PN)
  4. Check if the question statements have no conclusion combos (^Above rules)

if above things donot yield an answer, then we’ve to think about what will be the “conclusion(s)”?

Conclusive-Combos

If you’ve followed above steps, then question statements in the format “A to B and then B to C.”

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 mug-up rules as well.

Conclusive-CombosIn 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.

Try a question from SSC-CGL (Tier-I, 2010) exam,

DemoQ: Crazy men and Women

Question Statements

  1. All men are women.
  2. All women are crazy.

Conclusion

  1. All Men are crazy
  2. All the crazy are men
  3. Some of the crazy are men
  4. Some of the crazy are women

Answer

  1. None of the conclusion follows
  2. All conclusions follow
  3. Only 1, 3 and 4 follow
  4. Only 2 and 3 follow

(I suggest you pause here. First try to solve it on your own, without directly reading the solution. If you’ve difficulty, re-read rules given above)

Solution

Our standard operating procedure (SOP)
Question Statements

  1. All men are women.
  2. All women are crazy.

First step: make sure four terms are not given = check. Only three terms (men, women, crazy)
Second step, make sure they’re in standard format (A to B and then B to C): Check yes they’re.
Hence conversion is not required.

  1. All men(A) are women. (B) (UP)
  1. All women(B) are crazy.(C) (UP)

Third step, classify the statements.

  1. All men are women.
Universal Positive (UP)
  1. All women are crazy.
Universal Positive (UP)

Fourth step: check the combo for question statements.

  • Well, since it is UP+UP= its size doesn’t increase. Hence conclusion should be UP. (A to C) meaning All men(A) are crazy.(C)

Check the answer statements.

  1. All Men are crazy
Correct.
  1. All the crazy are men
Recall that “conversion table”.Universal Positive (UP) can be converted only into Particular Positive (PP).
Since All men are crazy => Some Crazy are men.
But we cannot say All crazy are men. So this option is false.
If you apply common sense at this stage: well, 1st statement correct, and 2nd statement is false, hence answer is (C): only 1, 3 and 4 follow!
  1. Some of the crazy are men
Correct because of “conversion table”
  1. Some of the crazy are women
Given question statement : All women are crazy. (Universal positive). If we apply conversion table (UP=> PP) then Some Crazy are women. Hence this statement is also correct.

Final answer (C): only 1, 3 and 4 follow
If you’re still staggering, I suggest you go through those rules again, note them down in a diary in your own words and language, revise a few times. Then try next question

DemoQ: Intelligent Poets and singers

Question Statements (SSC-CPO exam)

  1. All poets are intelligent
  2. All singers are intelligent.

Conclusion

  1. all singers are poets
  2. some intelligent persons are not singers

Answer choices

  1. only conclusion one follows
  2. only conclusion two follows
  3. either conclusion one or conclusion two follows
  4. neither follows

solution

first step: does the question statements have only three terms? Check: Yes. Singers, poets, intelligent. Good, proceed with next step.
Second step: Are the question statements given in standard format (A to B then B to C)?
Check. Nope

  1. All poets (A) are intelligent (B)
  2. All singers (C) are intelligent. (B)

Then we have to convert it into standard format. And since both statements are universal positive, we don’t need to worry about which statement to convert first? (that “priority order”, more about it, explained at the bottom of this article.)
Second statement is universal positive (UP), according to our table, we can only convert it into particular positive (PP) therefore
All singers (C) are intelligent. (B)==> Some intelligent persons(B) are singers.(C)
Now the new question statements, in the standard format (A to B then B to C) are
1. All poets are intelligent (B)
2. Some intelligent persons(B) are singers.
Third step, classify the question statements

question statementtype
1. All poets(A) are intelligent (B)Universal positive (UP)
2. Some intelligent persons(B) are singers.(C)Particular positive (PP)

Fourth step, apply the combo rules.
Since UP’s politicians hate particular statements (both positive and negative), hence no conclusion can be drawn. That means we cannot connect A to C or C to A.
Now check the Answer statements

i. all singers(C) are poets (A)
  • False. UP+PP=no conclusion, as explained above.
ii. some intelligent persons are not singers
  • Check the second original question statement : All singers are intelligent. (Universal positive –UP).
  • According to our conversion table, UP can be converted into particular positive (PP) only. But this answer statement (II) is a particular negative statement. Hence this is also false.

Final answer: (D) neither follows.

CAT-level

Same UP-UN Concept but they pack 3-4 or more syllogism questions into one question to test your speed, not just your understanding. for example:

DemoQ: Sweet Testing Apples (CAT)

given question has five statements followed by options containing three statements put together in a specific order. Choose the option which indicates a valid argument, where the third statement is a conclusion drawn from the preceding two statements.
Question statements (CAT 1999)

  1. Apples are not sweet
  2. Some apples are sweet
  3. All sweets are tasty
  4. Some apples are not tasty
  5. No apple is tasty

answer choices

  1. cea
  2. bdc
  3. cbd
  4. eac

solution and approach

we’ve to check the given options one by one.
Option (i). CEA. Meaning we’ve to take C as our statement (I), E as our Statement (II) and then observe, if statement (A) can be concluded from C and E.

CAll sweets are tastyUniversal positive
ENo apple is tasty.Universal negative
AApples are not sweetUniversal negative

In the actual CAT exam, we cannot afford to waste time in actually converting all statements and checking them.
Here is the fast approach
1. three terms?= yes
2. in standard format? No. but we can convert second (UN) into another UN and then combo rule is UP+UN=UN.
Hence this answer choice (CEA) is correct.
Final answer (i) CEA

DemoQ: Working mother nurses (CAT)

question statementanswer choices
  1. No mother is a nurse.
  2. Some Nurses like to work
  3. No woman is prude
  4. Some prude are also nurses
  5. Some nurses are women
  6. All women like to work
  1. ABE
  2. CED
  3. FEB
  4. BEF

Check the answer choices one by one.

i. ABE

A (Statement I)No mother is a nurse. (UN)
B (Statement II)Some Nurses like to work
E (Conclusion)Some Nurses are women.

This is invalid. Because Statement I and II have three terms (Mother, Nurse and work) while given conclusion statement adds fourth new term “women”

Move to next choice.

ii. CED

StatementType
C (Statement I)No woman is prudeUniversal negative
E (Statement II)Some nurses are womenParticular positive
D (conclusion)Some prude are also nursesParticular positive

Question statements have three terms? Yes (women, prude, nurses)
Are they in standard format (A to B then B to C?) nope.

No woman(B) is prudeUniversal negative
Some nurses are women(B)Particular positive

change position of first and second statement.
1. Some nurses(A) are women(B)
2. No woman(B) is prude(C)

question statementtype
1. Some nurses(A) are women(B)Particular positive (PP)
2. No woman(B) is prude(C)Universal negative (UN)

Apply the combo rules
PP+UN=??

  • When Mr.PP observes the universe via NASA telescope, his mood becomes particularly negative or positive depending on the mood of universe. Hence PP+UN=PN.(A to C)
  • So legitimate conclusion is “Some Prune arenot nurses”.
  • But Check the given conclusion statement: “Some prude are also nurses.” It is Particular positive (PP).
  • But According to conversion table, PN cannot be converted. So we cannot say that since “Some prune are not nurses, that means some prunes are nurses!”
  • Therefore given answer choice(ii) CED is false because D cannot be concluded from C+E.
  • Move to the next answer choice.

Actual thought process: three terms =yes. Standard form=no. rearrange. But PP+UN=PN, can’t be converted to PP. Hence false.

iii.FEB

StatementType
F (Statement I)All women like to workUniversal positive UP
E (Statement II)Some nurses are womenParticular positive PP
B (conclusion)Some nurses like to workParticular positive PP

three terms =yes. Standard form=no. but no need to convert, just exchange position of statement I and II.

Some nurses(A) are women(B)Particular positive PP
All women(B) like to work (C)Universal positive UP

Apply combo rule, again same situation
When Mr.PP observes the universe via NASA telescope, his mood becomes particularly positive or negative depending on the mood of universe. Hence PP+UP=PP.(A to C).
Some nurses(A) like to work(C). Done! This is same as the given conclusion (B)
Therefore, final answer is (iii) FEB.

DemoQ: 4 questions in 1!

This one is from CAT-1999.
Each of the given question statement as three segments. Choose the alternative where third segment of the statement can be logically be used using the both preceding two but not just from one of them
Question statements

  1. all dinosaurs are prehistoric creatures. Water buffaloes are not dinosaurs. Water buffaloes are not prehistoric creatures
  2. all politicians are frank. No frank people are crocodiles. No crocodiles are politicians
  3. no diamond is quartz. No opal is quartz. Diamonds are opals.
  4. All monkeys like bananas. Some Joes like bananas. Some Joes are monkeys.

Answer choice

  1. Only C
  2. Only B
  3. Only A and D
  4. Only B and C

Approach

C. Diamonds, Quartz, Opals.Three terms yes. Standard format =No.Both question statements are Universal negative. We can convert either of them, into UN or PN. But in any case, both question statements will remain negative. And Two negatives=no conclusion. So “C” is not possible. Hence answer choice (i) and (iv) eliminated.
B. Frank politicians and crocodilesAlready in three terms standard format.UP+UN=size enlarged and becomes UN.
So conclusion should be “No crocodile is politician” so this statement is correct. Hence answer choice (ii).

Final answer: (ii) only B.
The End?
No. Picture abhi baaki hai mere dost: just three more concepts before concluding the Two-Statement Syllogism

Special Conversions

Recall that when question statements are not in standard format (A to B then B to C), in that case we’ve to convert them according to conversion table. Here are some special cases.

Given Question statementConversion (all applicable to all given question statements)Type
  • None but Politicians are honest.
  • No one else but Politicians are honest.
  • Only politicians are honest.
  • Politicians alone are honest
  1. All honest(people) are politicians
UP
  1. No non-politician is honest.
  2. No honest (people) are non-politicians.
UN
  1. Some politicians are honest
PP

Second concept:

Complimentary pairs

Earlier we saw there are five no-conclusion combos

  1. UP’s politicians hate giving particular statements (both positive and negative). E.g. they donot reveal their clear position on FDI in retail until the 11th hour.
  2. United Nations hates negativity of any type. (both Universal and particular)
  3. Pritish Nandy hates everybody.
  4. Two-negatives=no conclusion.
  5. Two particulars=no conclusion.

For example

Question statement1. Some Politicians are male.2. Some males are honest.
Conclusion1. Some Politicians are honest.2. No Politicians are honest.

Answer choice

  1. Only 1 follows
  2. Only 2 follows
  3. Either 1 or 2 follows
  4. Neither follows

Apply the standard operating procedure:
Three terms? Check: yes
Are they in standard format? A to B then B to C? check. Yes
Then classify the statements

1. Some Politicians(A) are males(B)Particular positive.
2. Some males(B) are honest(C)Particular positive.

From the given rules, Two particulars = No conclusion!
But please observe one of the answer choice (C)= Either 1 or 2 follows.
Consider these cases

Case#2

PoliticiansMaleshonest
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Raja
  4. Kalmadi
  5. Sheila
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Raja
  4. Kalmadi
  5. Bhagat Singh
  6. ChandraSekhar Azad
  1. Sardar Patel
  2. Lal Bahadur Shastri
  3. Bhagat Singh
  4. ChandraSekhar Azad
  5. Sarojini Naidu
  6. Mother Teresa

In this case#1: some politicians (Sardar and Shastri) are honest.
So “conclusion (1) may be possible.”

Case#2

PoliticiansMaleshonest
  1. Raja
  2. Kalmadi
  3. Sheila
  1. Raja
  2. Kalmadi
  3. Bhagat Singh
  4. ChandraSekhar Azad
  1. Bhagat Singh
  2. ChandraSekhar Azad
  3. Sarojini Naidu
  4. Mother Teresa

In this case, No politician is honest.
So “conclusion (2) may be possible.”
Therefore answer becomes “Either 1 or 2 follows”
Such syllogism-situations are called “complementary”.
You’ve to check following things, before thinking about “complementary” cases.

  1. Two statements with three terms? Yes
  2. Question statements are given in standard format (A to B Then B to C). if not, then rearrange or convert them.
  3. Classify the statements (UP, UN, PP, PN)
  4. Apply the rules. Get the answer.
  5. If Step #4 gives “No conclusion” AND one of the answer choice is in the format of “Either I or II follows”, only then check for complemantary case.

Checklist: complementary case

  1. Two answer choices have same subject and predicate.
ApplicableNot applicable
1. Some Politicians are honest.2. No Politicians are honestBecause both have common subject (politician) and common predicate (honest)1. Some Politicians are honest.2. No Honest are Politicians.In first statement, subject=Politician but in second statement, subject= Honest. Hence complemantary case not possible.

2). The answer choice combo must be either of these three

Answer choice comboexample
Uttar Pradesh (UP) + Pritish Nandy (PN)1. All Politicians are honest.
2. Some Politicians arenot honest
PP + Pritish Nandy (PN)1. Some Politicians are honest.
2. Some Politicians arenot honest
PP + United Nations (UN)1. Some Politicians are honest.
2. No Politicians are honest

When these two conditions are met, then answer would be “Either (I) or (II) follows.”

Priority order

You know that when Question statements are not in standard format (A to B Then B to C), we must convert them. But here is a thing to keep in mind. Consider these statements

Question statements:
1. All Dogs are Cats.
2. Some Dogs are Pigs.
Common term or middle term is Dogs. So that’s our “B”.
1. All Dogs(B) are Cats.
2. Some Dogs(B) are Pigs.
We can convert it via two routes

Route #1Route #2
Just convert the first statement.
1. Some Cats are dogs. (Rule: UP to PP)
2. Some Dogs are pigs.
We’ll re-order the statements. (that is interchange thee position of both statements)
1. Some dogs(B) are pigs
2. All Dogs(B) are Cats
Now we’ll convert the first statement.
1. Some pigs are Dogs (B) (Rule: PP to PP)
2. All dogs (B) are cats.

Both routes are valid.
Now the question is, which route should be preferred?
The priority order is:
1) Particular positive (PP) >> 2) Universal Negative (UN) >> 3) Universal Positive (UP)
Note: we’ve not included Particular Negative (PN) in this order because PN cannot be converted. So according to this priority order PP>UN>UP, route #2 is the more suitable approach. (although such complications don’t usually arise in most of the questions).

Tricky Situations: Priority order

Consider this scenario

Question statementsConclusion
  1. All women(B) are birds
  2. Some women(B) are tree
  1. Some birds are tree
  2. All trees are bird.

As you can see, the question statements are not in standard format (A to B then B to C).

So, which question statement to convert?

First the wrong approach.

WRON

G

Since question statements are not in standard format (A to B then B to C), hence we’ll convert first statement. (UP to PP)After conversion

  1. Some birds(A) are women (B)
  2. Some women(B) are tree

Both question statements are particular, hence final answer=No conclusion. (please note: this approach is wrong, because we’ve not followed the priority order).

Now the correct approach

CORR

E

C

T

The priority order for Statement conversion is PP>UN>UP.Meaning, if there are two question statements, and we’ve to convert one of them to make it a standard format=> then we’ll convert Particular positive statement first.So in the given case

  1. All women(B) are birds
  2. Some women(B) are tree

Convert second statement. (PP to PP)

  1. All women(B) are birds.
  2. Some trees are women(B).

Now exchange positions of question statements

  1. Some trees are women(B). (PP)
  2. All women(B) are birds. (UP)

Now they’re in standard format, apply combo rule: PP+UP=PP (Nasa telescope rule!)

Hence conclusion is

Some trees are birds. (PP)

We can also say that Some birds are trees. (PP to PP conversion). Therefore answer is (1)

Moral of the story: Conversion priority: PP>UN>UP. Especially when you’re getting PP+PP= no conclusion after conversion.

Tricky Situations: 1-Statement Conclusion

Question statementsConclusion
  1. All the flowers are leaves.(B) (UP)
  2. Some leaves(B) are birds (PP)
  1. Some birds are flowers
  2. Some leaves are flowers

Question statement contains only three terms=yes.

Are they in standard format? (A To B then B to C?) =Yes.

Apply combo rules: UP+PP=No conclusion because Uttar Pradesh’s politicians hate particular statements.

But here’s the catch. Observe the conclusion statements carefully

Conclusion statementThought process
  1. Some birds are flowers
Not possible because combo rule.
  1. Some leaves are flowers
first question statement says All flowers are leaves. If you apply the conversion rule UP->PP, thenAll flowers are leaves=> Some leaves are flowers. Hence this conclusion is correct, although it did not employ both question statements.

Moral of the story: Read terms (subject-predicate) of  conclusion statements.

Summary

What to do when 2-statement syllogism question is given?

  1. They must have only three terms (A, B and C)
  2. Are the question statements in standard format (A to B then B to C)? if no, then refer to following conversion table. (important: priority order for conversion is PP>UN>UP.)
TypeValid Conversion
Universal Positive (UP)Only PP
Universal Negative (UN)PN or UN
Particular Positive (PP)Only PP
Particular Negative (PN)Can’t do.

3. Classify the Question statement (UP, UN, PP, PN)
4. Apply the combo rules on Question statements.

No conclusion

Yes conclusion

  1. UP’s politicians hate giving particular statements (both positive and negative). E.g. they donot reveal their clear position on FDI in retail until the 11th hour. (UP+PP/PN=NO)
  2. United Nations hates negativity. (both Universal and particular)(UN+UN/PN=NO)
  3. Pritish Nandy hates everybody. (first statement is PN=NO, Irrespective of second statement.)
  4. Two-negatives=no conclusion.
  5. Two particulars=no conclusion.
  1. If Uttar Pradesh meets Uttar Pradesh, then its size doesn’t increase. (UP+UP=UP)
  2. If Uttar Pradesh meets United Nations then size increases and it becomes United Nations. (UP+UN=UN)
  3. 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). (UN+UP/PP=PN)
  4. When Mr.PP observes the universe via NASA telescope, his mood becomes particularly positive or negative depending on the mood of universe.(PP+UP/UN=PP/PN)

5. (rarely required): if no-conclusion and “either or” given in answer, then check for Complimentary case.

This concludes the discussion on 2 statement Syllogism question.
In later article, we’ll see the 3-statement syllogism. It is basically extention of the same UP-UN method that we learned here. However, to quickly solve 3-statements, first you must become a master of 2-statement. So, practice as many sums as you can, from any of the following books.

RS Sijwali MK Pandey Syllogism
For the whole archive of Aptitude related articles, visit Mrunal.org/aptitude





So far 573 Comments posted

  1. Aj

    Stat : All bags are cakes. All lamps are cakes.
    Conc: some lamps are bags. No lamp is bag.
    Aftr conversion it forms UP+PP pair.

    However in the ans it was given that these form a complimentary pair, but above post mentions that only (UP+PN,PP+PN,PP+UN) forms a complementary pair. Pls let me know ur thoughts else corect me if im wrong

  2. mohit chauhan

    Hi Mrunal,

    Must say, a great post on 2 statement syllogism. Tremendously helpful. However, nowadays even in PO exams, mostly three to four statement syllogisms are appearing frequently. So, can u please provide posts on three statement and four statement posts?

  3. AJAY KUMAR

    Statements: Some institutes are banks.
    All institutes are academies.
    All academies are schools.

    Conclusions:
    I. All banks can never be schools.
    II. Any bank which is an institute in a school

    How analyse 2nd Conclusion through UP-UN method, because it consist three terms BANK,INSTITUTE AND SCHOOL
    PLZ help anyone

  4. AJAY KUMAR

    Sir Please explain how to solve Syllogism based on Possibility

    (1) If only conclusion I follows
    (2) If only conclusion II follows
    (3) If only conclusion I or II follows
    (4) If neither conclusion I nor II follows
    (5) If both conclusions I and II follows

    (Q. 1 2)
    Statements: A. Some poor are rich
    B. All rich are doctors.
    C. Some intelligent are doctors.

    1. Conclusions: I. At least some poor are intelligent.
    II. All intelligent being rich is a possibility.

    2. Conclusions: I. All intelligent being doctors is a possiblity.
    II. Some poor are doctors.

  5. alka thakur

    what about PP+PP case and which needs conversion moreover and have complimentary pairs too in conclusion?

  6. anindya

    mrunal sir, please make a video on syllogism…..i am telling because it will be more helpful if u provide a video and make us understand more clearly what is written on here….so its my ardent request to u,sir….(exactly like trigonometry height and distance,it is crystal clear to me now :p
    )

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