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

1. Introduction

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

DemoQ: Sweet Testing Apples (CAT)

DemoQ: Working mother nurses (CAT)

DemoQ: 4 questions in 1!

11. Special Conversions

12. Complimentary pairs

13. Tricky Situations: Priority order

14. Tricky Situations: 1-Statement Conclusion

15. Summary

Introduction

There are two main types of Syllogism question

2-Statements 3-Statements

Question Statement:I. All cats are dogsII. All dogs are birdsConclusion:I. Some cats are birdsII. Some birds are cats.

Question StatementA. All cats are dogsB. some pigs are catsC. no dogs are birdsConclusionI. some cats are dogsII. no birds are catsIII. some pigs are birdsIV. some pigs are not birds

2 Statement Syllogism questions are usually found in IBPS (Bank) and SSCexams.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 firstmaster the 2-statement technique here.)

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

1. VennDiagram

In the exam, Have to think of all possible “Venn-Diagram”situation and draw them to check every statement.= timeconsuming in the exam hall.

2. AEIO(analyticalMethod)

Have to mugup some rules, and spend some hours @home tomaster the “AEIO” conversion in your head. But once done, itis easy as a walk in the park.

3. Distributionof terms(Tickmethod)

Usually taught in CAT coaching classes and study material.Technique is very fast but It excludes the concept of“Conversion” and “Complementary cases”, hence sometimesmakes it difficult to solve non-CAT questions.

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

Basics

Subject vs Predicate

Consider this question statement1. All cats are dogs2. Some dogs are birds3. No bird is a pig4. 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 MadhuKoda – first term is subject and second term is predicate.Let’s relook at those question statements

Subject Predicate

1. All cats are dogs Cats Dogs

2. Some dogs are birds Dogs Birds

3. No bird is a pig Bird Pig

4. Some pigs are not birds.Pigs Birds

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,

Xyz Subject Is/are (+/-not) Predicate

All Cats Are Dogs

Some Pigs Are not birds

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

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

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

All, every, any, none, not a single, only etc.Universal (positiveor negative)

Some, many, a few, quite a few, not many, very little, most of,almost, generally, often, freqently, etc.

Particular (positiveor 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 is1. A—>B2. 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 issaved! Just tick the answer “no conclusion can be drawn”.

For example

Questionstatements

Answer

1. All cats areDogs2. Some birds arepigs

No conclusion can be drawn. Because it has four terms (cats, dogs,birds, pigs)A–>BC–>D

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

1. A—>B2. B—>C

1. First term—>Middle Term2. Middle Term—>Third term

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

Given question statements are1. A—>B2. C—>B

This must be converted into1. A—>B2. B—>C

Given question statements are1. B—>A2. B—>C

This must be converted into1. A—>B2. B—>C

Ok, so how to convert the statements?

Universal Positive (UP)

Given Statement Valid conversions Type

Given Statement: All Cats are DogsSome Cats are dogs Particular Positive (PP)

Some dogs are cats Particular 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 “Allcats are dogs”. (Only A is B –> All B are A)

Universal Negative (UN)

Given Statement Valid conversions Type

Given Statement: No Cats are DogsSome dogs are not cats Particular Negative (PN)

No dogs are cats Universal Negative (UN)

It means UN can be converted into PN or UN.

Particular Positive (PP)

Given Statement Valid conversions Type

Some Cats are Dogs Some dogs are cats Particular Positive (PP)

It means PP can be converted into PP only.

Particular Negative

Example: Some Cats are not Dogs. In Particular negative statements (PN), noconversion can be made.So PN=can’t convert.To sum up the conversion rules

Type Valid 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. ForexampleQ. What can be concluded from the given statement: “Some Politicians are honestmen.”Answer choices

1. Some Honest men are not Politicians.2. All Honest men are not politician3. 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 positivestatement (PP).Hence according to our table, it can be converted into PP only. Therefore

Given answer choice Thought process

1. Some Honest men are notPoliticians.

Particular negative (PN), hence eliminate.

2. No Honest men are politicians. Universal Negative, hence eliminate

3. Some Honest men are politicians.PP hence this is correct answer.

4. None of Above.–not applicable because C is the correctanswer.

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 Patel2. Lal Bahadur Shastri3. Raja4. Kalmadi

Predicate (Honest Men)1. Sardar Patel2. 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 politicianset.

Case #2

Data

Subject (Politicians)

1. Sardar Patel2. Lal Bahadur Shastri3. Raja4. Kalmadi

Predicate (Honest Men)

1. Sardar Patel2. Lal Bahadur Shastri3. Bhagat Singh4. 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’ concludeone 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 Statement Valid Conversion Path

Universal Positive (UP)

All cats(A) are dogs (B)

Only PP

Some Cats (A) are dogs. (B)

Some dogs (B) are cats. (A)

A to B

B to A

Universal Negative (UN)

No Cats(A) are dogs (B)

PN :Some Dogs (B) are not Cats (A).

B to AUN: 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 question2. Subject vs predicate3. Type of statements (UP, UN, PP, PN)4. Standard format and conversion.

The standard question format isA–>BB–>CIf the given question doesn’t have statements in ^above standard format, then we mustconvert 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 statements Conversion?

1. All Cats are dogs(B)2. Some dogs(B) are notpigs.

Already in standard format (A to B and then B to C)hence no need to convert.

1. Some dogs(B) are notpigs.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 statementsyllogism question?

No conclusion Combos

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

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 ofthis 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 followthese 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 thenB to C.”

First statement (A to B)Second statement (B toC)

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 toA)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 firstquestion statement is Universal Negative (UN).Let’s condense this table into mug-up rules as well.

Conclusive-Combos In your head, visualize

1. UP+UP=UPIf Uttar Pradesh meets Uttar Pradesh, then its size doesn’tincrease.

2. UP+UN=UNIf Uttar Pradesh meets United Nations then its size increasesand it becomes United Nations.

3. UN+(UP/PP)=PN

United Nations Secretary Ban Ki Moon is in very positivemood. But he meets another positive person, and his attitudeis totally reversed- he becomes particularly negative!(reversed =C to A)

4. PP+(UP/UN)=PP/PN

When Mr.PP observes the universe via NASA telescope, hismood becomes positive or negative depending on the mood ofuniverse.

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 crazy2. All the crazy are men3. Some of the crazy are men4. Some of the crazy are women

Answer

a. None of the conclusion followsb. All conclusions followc. Only 1, 3 and 4 followd. Only 2 and 3 follow

(I suggest you pause here. First try to solve it on your own, without directly reading thesolution. 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 yesthey’re.Hence conversion is not required.

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

2. All women(B) are crazy.(C) (UP)

Third step, classify the statements.

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

2. 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 beUP. (A to C) meaning All men(A) are crazy.(C)

Check the answer statements.

1. All Menare crazy

Correct.

2. All thecrazy aremen

Recall that “conversion table”.Universal Positive (UP) can beconverted 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!

3. Some ofthe crazyare men

Correct because of “conversion table”

4. Some ofthe crazyarewomen

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 followIf you’re still staggering, I suggest you go through those rules again, note them down ina 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 poets2. some intelligent persons are not singers

Answer choices

a. only conclusion one followsb. only conclusion two followsc. either conclusion one or conclusion two followsd. 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 toC)?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 areuniversal 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 onlyconvert it into particular positive (PP) thereforeAll 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) are1. All poets are intelligent (B)2. Some intelligent persons(B) are singers.Third step, classify the question statements

question statement type

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), henceno 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. someintelligentpersons are notsingers

Check the second original question statement : All singers areintelligent. (Universal positive –UP).According to our conversion table, UP can be converted intoparticular positive (PP) only. But this answer statement (II) is aparticular 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 onequestion 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 puttogether 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)

a. Apples are not sweetb. Some apples are sweetc. All sweets are tastyd. Some apples are not tastye. No apple is tasty

answer choices

1. cea2. bdc3. cbd4. 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 tasty Universal positive

E No apple is tasty. Universal negative

AApples are not sweet Universal negative

In the actual CAT exam, we cannot afford to waste time in actually converting allstatements and checking them.Here is the fast approach1. three terms?= yes2. in standard format? No. but we can convert second (UN) into another UN and thencombo rule is UP+UN=UN.Hence this answer choice (CEA) is correct.Final answer (i) CEA

DemoQ: Working mother nurses (CAT)

question statement answer choices

a. No mother is a nurse.b. Some Nurses like to workc. No woman is pruded. Some prude are also nursese. Some nurses are womenf. All women like to work

1. ABE2. CED3. FEB4. 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

Statement Type

C (Statement I) No woman is prude Universal negative

E (Statement II) Some nurses are women Particular positive

D (conclusion) Some prude are also nurses Particular 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 prude Universal 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 statement type

1. Some nurses(A) are women(B) Particular positive (PP)

2. No woman(B) is prude(C) Universal negative (UN)

Apply the combo rulesPP+UN=??

When Mr.PP observes the universe via NASA telescope, his mood becomesparticularly negative or positive depending on the mood of universe. HencePP+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 isParticular positive (PP).But According to conversion table, PN cannot be converted. So we cannot saythat since “Some prune are not nurses, that means some prunes are nurses!”Therefore given answer choice(ii) CED is false because D cannot be concludedfrom C+E.Move to the next answer choice.

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

iii.FEB

Statement Type

F (Statement I) All women like to work Universal positive UP

E (Statement II) Some nurses are women Particular positive PP

B (conclusion) Some nurses like to work Particular positive PP

three terms =yes. Standard form=no. but no need to convert, just exchange position ofstatement 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 situationWhen Mr.PP observes the universe via NASA telescope, his mood becomesparticularly positive or negative depending on the mood of universe. HencePP+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 wherethird segment of the statement can be logically be used using the both preceding twobut not just from one of themQuestion statements

a. all dinosaurs are prehistoric creatures. Water buffaloes are not dinosaurs. Waterbuffaloes are not prehistoric creatures

b. all politicians are frank. No frank people are crocodiles. No crocodiles arepoliticians

c. no diamond is quartz. No opal is quartz. Diamonds are opals.d. All monkeys like bananas. Some Joes like bananas. Some Joes are monkeys.

Answer choice

i. Only Cii. Only B

iii. Only A and Div. Only B and C

Approach

C. Diamonds,Quartz,Opals.

Three terms yes. Standard format =No.Both question statements areUniversal negative. We can convert either of them, into UN or PN. Butin any case, both question statements will remain negative. And Twonegatives=no conclusion. So “C” is not possible. Hence answer choice(i) and (iv) eliminated.

B. Frankpoliticiansandcrocodiles

Already in three terms standard format.UP+UN=size enlarged andbecomes UN.So conclusion should be “No crocodile is politician” so this statementis correct. Hence answer choice (ii).

Final answer: (ii) only B.The End?No. Picture abhi baaki hai mere dost: just three more concepts before concludingthe 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 somespecial cases.

Given Question statement Conversion (all applicable to all given Type

question statements)

None but Politicians arehonest.No one else but Politiciansare honest.Only politicians are honest.Politicians alone are honest

1. All honest(people) are politicians UP

2. No non-politician is honest.3. No honest (people) are non-politicians.

UN

4. 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 statement 1. Some Politicians are male.2. Some males are honest.

Conclusion 1. Some Politicians are honest.2. No Politicians are honest.

Answer choice

a. Only 1 followsb. Only 2 followsc. Either 1 or 2 followsd. Neither follows

Apply the standard operating procedure:Three terms? Check: yesAre they in standard format? A to B then B to C? check. YesThen 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

Politicians Males honest

5. Sardar Patel6. Lal Bahadur Shastri7. Raja8. Kalmadi9. Sheila

1. Sardar Patel2. Lal Bahadur Shastri3. Raja4. Kalmadi5. Bhagat Singh6. ChandraSekhar Azad

1. Sardar Patel2. Lal Bahadur Shastri3. Bhagat Singh4. ChandraSekhar Azad5. Sarojini Naidu6. Mother Teresa

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

Case#2

Politicians Males honest

1. Raja2. Kalmadi3. Sheila

1. Raja2. Kalmadi3. Bhagat Singh4. ChandraSekhar Azad

1. Bhagat Singh2. ChandraSekhar Azad3. Sarojini Naidu4. 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? Yes2. 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.

Applicable Not applicable

1. Some Politicians are honest.2. NoPoliticians are honestBecause bothhave common subject (politician)and common predicate (honest)

1. Some Politicians are honest.2. No Honest arePoliticians.In first statement, subject=Politicianbut in second statement, subject= Honest.Hence complemantary case not possible.

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

Answer choice combo example

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 toC), we must convert them. But here is a thing to keep in mind. Consider thesestatements

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 #1 Route #2

Just convert the firststatement.1. Some Cats are dogs.(Rule: UP to PP)2. Some Dogs are pigs.

We’ll re-order the statements. (that is interchange theeposition of both statements)1. Some dogs(B) are pigs2. All Dogs(B) are CatsNow 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 beconverted. So according to this priority order PP>UN>UP, route #2 is the moresuitable approach. (although such complications don’t usually arise in most of thequestions).

Tricky Situations: Priority order

Consider this scenario

Question statements Conclusion

1. All women(B) are birds2. Some women(B) are tree

1. Some birds are tree2. All trees are bird.

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

So, which question statement to convert?

First the wrong approach.

WR

O

N

G

Since question statements are not in standard format (A to B then B to C), hencewe’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 priorityorder).

Now the correct approach

CO

R

The priority order for Statement conversion is PP>UN>UP.Meaning, if there aretwo question statements, and we’ve to convert one of them to make it a standardformat=> then we’ll convert Particular positive statement first.

So in the given case

1. All women(B) are birds2. Some women(B) are tree

Convert second statement. (PP to PP)

1. All women(B) are birds.

R

E

C

T

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 telescoperule!)

Hence conclusion is

Some trees are birds. (PP)

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

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

Tricky Situations: 1-Statement Conclusion

Question statements Conclusion

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

1. Some birds are flowers2. 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 hateparticular statements.

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

Conclusionstatement

Thought process

1. Somebirdsareflowers

Not possible because combo rule.

2. Some first question statement says All flowers are leaves. If you apply the

leavesareflowers

conversion rule UP->PP, thenAll flowers are leaves=> Some leaves areflowers. Hence this conclusion is correct, although it did not employboth 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 isPP>UN>UP.)

Type Valid 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 givingparticular statements (bothpositive and negative). E.g. theydonot 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 secondstatement.)

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 Nationsthen size increases and it becomesUnited Nations. (UP+UN=UN)

3. United Nations Secretary Ban Ki Moonis in very positive mood. But he meetsanother positive person, and his attitudeis totally reversed- he becomesparticularly negative! (reversed =C to A).(UN+UP/PP=PN)

4. When Mr.PP observes the universe viaNASA telescope, his mood becomesparticularly positive or negativedepending on the mood of universe.(PP+UP/UN=PP/PN)

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

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