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

MK Pandey Fast track to objective arithmetic
  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
  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 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

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 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 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

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 Statement Valid conversions Type
Given Statement: All Cats are Dogs Some 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 “All cats are dogs”. (Only A is B –> All B are A)

Universal Negative (UN)

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)

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), no conversion 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. 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 choice Thought 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 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 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 statements Conversion?
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-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.

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 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), 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.

C All sweets are tasty Universal positive
E No apple is tasty. Universal negative
A Apples are not sweet Universal 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 statement answer 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

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 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

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 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 crocodiles Already 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 statement Conversion (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 statement 1. Some Politicians are male.2. Some males are honest.
Conclusion 1. 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

Politicians Males honest
  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

Politicians Males honest
  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.
Applicable Not 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 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 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 #1 Route #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 statements Conclusion
  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.

WR

O

N

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

CO

R

R

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 statements Conclusion
  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 statement Thought 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.)
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 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 CSAT MK
For the whole archive of Aptitude related articles, visit Mrunal.org/aptitude
If you wish to discuss any Syllogism questions, post them on following thread Mrunal.org/aptitude: (No registration necessary. Just use your gmail/ facebook account)

Lucent General Knowledge Objective English

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अब तक 450 कमेंट्स लिखी गयी

  1. bhadra says:

    SOME MEN ARE BACHELORS
    ALL BACHELORS ARE NOT FLIRT
    conclusion
    1.Some men are not flirt
    2.All men are not flirt
    3.Some men are flirt

    Sir,How ALL..NOT.. problems can be solved?

    • Ganesh Babu S says:

      For this you can convert the second option to obverse. Means convert Not Flirt to Flirt. So All Bachelors are not flirt can be converted into “some bachelors are flirt”. And now its easy, if two particular statements are used then no conclusion follows. So it becomes easy to answer. Hope it helps.

      • Vijender says:

        All bachelors are not flirt is an I type hidden proposition and It at best means “Some bachelors are not flirt”
        Three Ven diagram representation are possible for this proposition and all of them support SOME BACHELORS ARE NOT FLIRT”. Therefore Some Bachelors are flirt is not right…..

        • abhishek pandey says:

          in reasoning it cant be said “some bachelors are flirt” if given “all bachelor are not flirt” it should be said “no bachelor is flirt”
          now it is easy to solve and CONCLUSION 1 should be the right answer

    • tas says:

      Sir’s method is perfect

      But I am facing problem solving some questions.
      As per venn diag C1 shld be correct

  2. Deepak says:

    This is the best concept one can hope to find. Now that I can tackle these waiting for three statement ones.
    The concept really blew my mind

  3. A Sahoo says:

    Sir can u plz tell me the most probable essay topics for CPF 2013 exam. I have only few days left. Regards

  4. bhushan says:

    SOME MEN ARE BACHELORS
    ALL BACHELORS ARE NOT FLIRT
    conclusion
    1.Some men are not flirt
    2.All men are not flirt
    3.Some men are flirt
    :(
    :(

  5. chandrika says:

    thank you sir this approach really helps me.But still i am having problem in either or condition..
    Please help me…

  6. Vijender says:

    Hello Mrunal Sir, great work..
    But I think there is one mistake in one of your conclusions..
    PN + Anything = No Conclusion..
    (Pritish Nandy hates everybody)

    But Consider this
    some Animals are not pet.
    all dogs are pet.

    Conclusion : – Some Animals are not dogs..
    This is a valid conclusion as dogs being a subset of pet. We can safely conclude Some Animals are not dogs.
    So PN + UP = PN ( In case in both the premises Predicate is same))

    Analytically it can be understood as
    Some Animals are not pet => Some Animals are non Pet (BY OBVERSION) === PP Statement…
    All Dogs are Pets => No Dog is Non Pet (Again By Obversion ======= UN Statement….

    No Dog is Non Pet + Some Non Pet are Animals = (UN+PP = PN*)
    Which is “Some Animals are not Dogs”, the same as our conclusion.

  7. rishu says:

    mrunal sir…plzz tell strategy of ssc chsl exam

  8. manoj prabhakar says:

    somebody plzz help with the rules to deal with POSSIBILITY CASE conclusion

  9. rohit kundu says:

    One question Pls help…
    statement : 1.all pigs are elephant . 2. no pigs are bakers.
    conclusion 1. some bakers are not pigs. 2. some pigs are not bakers. 3. some some elephants are not baker 4.some bakers are not elephant.option a. 1,2 and 3 follow. B. 1,2 and 4 follow. C. 1,3 n 4. D. 2 ,3 n 4 . E. All follow.

    • Gopinath.R says:

      all follow

  10. kriti says:

    Great!!!! Just too good.. Really helpful. Thumbs up.

  11. Ram says:

    Dear Mrunal sir,
    can u please check it and tell me how this answer is right?
    we dont have any combo rule by using pn+?
    but how this answer comes?

    a. Some books are no reference books.
    b. All books are encyclopedias.
    Answer: Some reference books are no encyclopedias is correct!

    Some reference books are no encyclopedias
    No reference books are encyclopedias
    All reference books are encyclopedias
    None of the above

  12. Victor says:

    I got stuck in problem…

    2.Statements: All bags are cakes. All lamps are cakes.
    Conclusions:
    I.Some lamps are bags.
    II.No lamp is bag.
    (A) If only conclusion I follows
    (B) If only conclusion II follows
    (C) If either I or II follows
    (D) If neither I nor II follows and
    (E) If both I and II follow.

    Not in a standard format of A->B, B->C, so Cakes (B) and now
    All bags are cakes. UP
    All lamps are cakes. UP need to convert it to PP: Some cake are lamps
    Now UP+PP=No conclusion… what am i doing worng???

    • Tilak says:

      Dear,
      Both statements are UP and not in standard format. you are doing correctly but you have mistaken.
      Both conclusion are not true but in pair of complementry case hence, either or follow.

      • Victor says:

        Thanks Tilak
        Still have a doubt (question). During the discussion of the main article this case is not mentioned (either or). So when to come on this conclusion of either or, is there any standard rule just like all other rules discussed in this article.

      • Victor says:

        Sorry Tilak.

        I guess I was too eager to solve the question and hence overlooked the complementary pair discussion in the article. My fault. Thanks for helping me.

    • Tilak says:

      Further, just remember one thing if middle term is not distributed in any statement, then no conclusion b/w subject and predicate. This will save your time and you have to go fast solving approach.

      • ramesh says:

        all jugs are glasses
        ii.all glasses are cups
        iii.all jugs are pens
        conclution
        i.all pens are jugs
        ii.some glasses are pens
        iii.some cups are pens
        iv. all pens are cups

        none follows OR ii and iii follow

  13. Victor says:

    Statements: All fishes are grey in colour. (UP: B->C)
    Some fishes are heavy. (PP: B->A, priority for conversion, make PP and become statement one “Some heavy are fishes”)
    Conclusions:
    I.All heavy fishes are grey in colour.
    II.All light fishes are not grey in colour.
    SO PP + UP = PP (Some heavy are grey in colour, but answer is “a”)

    a. Onlt I follow
    b. Only II follow
    c. Either I or II follow
    D. Neither I not II follow
    E. Both I and II follow

    How to solve this as Statement I. have all A, B and C.

    • Nitish says:

      Any solution for this problem

  14. Prashant Kumar says:

    Thank You sir for the great lecture. I finally have some confidence that I can also some questions on syllogism correctly. Thanks a lot. May God Bless you

  15. sunil says:

    well explained. thanx

  16. ramesh says:

    i. all jugs are glasses
    ii.all glasses are cups
    iii.all jugs are pens
    conclution
    i.all pens are jugs
    ii.some glasses are pens
    iii.some cups are pens
    iv. all pens are cups

    none follows OR ii and iii follow

  17. ramesh says:

    please answer

  18. amit shukla says:

    Statements
    some chairs are doors.
    some doors are walls.
    some walls are pen.
    Conclusions:
    Some Pens are doors
    No pen is door
    Answers> Conclusion 1 is follows
    conclusion 2 follows
    either 1 or 2 follows
    neither 1 nor 2 follows
    both follows.
    Kindly explain which conclusion is follows.

    • Gopinath.R says:

      ans c

  19. tas says:

    Statement 1: All puppets are doll(UP)
    Statement 2: all dolls are toys(UP)

    conclusion 1: some toys are puppets( C to A)/PP
    conclusion 1I: all toys are puppets( C to A)/UP

    Answer: I is correct ( R S AGARWAL pg 5)

    acc. to rule

    UP + UP= UP( A to C)

    SO NONE conclusion shld follow

    Sir plzz explain

  20. tas says:

    one more question…..pg 7 R s agarwal

    S 1: lawers married only fair girls(UP)
    S 2: Shoba is a fair girl(UP)

    C 1: shobha was married to a lawyer (UP)
    C 2: Shobha was not married to a lawyer(UN)

    answer= either C 1 or C 2

    SINCE UP + UP= UP
    then only C 1 should be the answer

    sir plz explain

    • tas says:

      sorry typing mistake….

      correct S2 is

      S2 :shobha is very fair

  21. tas says:

    one more question…..pg 7 R s agarwal

    S 1: all students in my class are intelligent(UP)
    S 2: rohit is not intelligent(PN)

    C 1: rohit is not a student of my class(PN)
    C 2: rohit must work hard(PP)

    answer= only C 1 follows

    S 1(UP) should be converted to PP and both the statements should be re arranged

    so finally

    S1 : rohit is not intelligent(PN)
    S 2: SOME INTELLIGENT IN MY CLASS ARE STUDENTS (PP)

    so PN + PP = NO CONCLUSION SHOULD BE THE ANSWER

    why am I wrong Sir???????????/

  22. amit says:

    dear sir in complementary combo

    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.

    but in some books (class matterial ) it’s also possible please give me right one approch

    • Palanisamy says:

      Amit,

      In my opinion,

      2nd Statement can be re-written as No politicians are honest (UN to UN), by that way both the statements would have same subject and predicate satisfying the condition for Complementary case. Mrunal sir correct us if you find it as mistake.

      Regards,
      Palanisamy

  23. vinay sai says:

    Thanx a lot. The info provided fetched me a lot.

  24. Palanisamy says:

    Dear Mrunal Sir,

    The below question could be solved by tick mark and Venn diagram approach but not via UP-UN method. Could you help identify any mistake with my approach.

    PROBLEM# 1 – Question Statements:
    1) All pens are book (UP)
    2) Some pens are not pencils (PN)

    PROBLEM# 1 – Conclusion statement:
    Some books are not pencils

    PROBLEM# 1 – By UP-UN method,
    Rewriting statement# 1 UP to PP -> Some books are pen (PP)
    Cannot rewrite stmt# 2 as it is PN -> Some pens are not pencils (PN)

    PP+PN – No conclusion, but by both venn diagram approach and tick mark method the conclusion statement obtained is “Some books are not pencils”. I am assuming the problem with rewriting UP to PP but could you clarify please.

    Thanks,
    Palanisamy

  25. Palanisamy says:

    Dear Mrunal Sir,

    This is one other kind of issue. Posting it separate as the scenario is different from that of the one posted before.

    PROBLEM# 2 – Question Statements:
    1) Some T are not S (PN)
    2) All R are S (UP)

    PROBLEM# 2 – Conclusion statement:
    Some T are not R

    PROBLEM# 2 – By UP-UN method,
    Cannot rewrite stmt# 1 as it is PN -> Some T are not S (PN)
    Rewriting statement# 2 UP to PN -> Some S are R (PP)

    PN + PP = No conclusion. So how to solve this problem via UP-UN approach? Both venn diagram approach and tick mark method provides the conclusion statement as “Some T are not R”. Could you help clarify please.

    Regards,
    Palanisamy

  26. mohini mhetre says:

    Very nice artical…This was really useful for me…thank you so much.

  27. Saravana Guru says:

    Syllogism was always a confusing topic for me. Mrunal Sir, u made it so easy with this wonderful article. Your method to remember conversions is creative and perfect. Now, I find pretty much easier to solve them. Thank a lot. Salute to your meticulous effort in creating such a wonderful, satirical and informative website. My small suggestion

    Non-Conclusive combos can be derived from conclusive combos and thus need not necessarily required to be remembered.

    UP + UP = UP
    UP + UN = UN

    Among UP, PP, UN and PN if we see, UP and UN are used and the left out are PP and PN
    Hence, UP + (PP/PN) = No conclusion

    Similiarly, UN + (UP/PP) = UN, Hence UN + (UN/PN) = No conclusion (UN and PN are left out in conclusive combos)

    Conclusive Combos Non-Conclusive combos

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

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

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

    PN + (UP/UN/PP/PN)

  28. Shivraj says:

    Question Statements (SSC-CPO exam)

    All poets are intelligent
    All singers are intelligent.

    Conclusion

    all singers are poets
    some intelligent persons are not singers

    Answer choices
    only conclusion one follows
    only conclusion two follows
    either conclusion one or conclusion two follows
    neither follows

    How is the answer for this question is 4–> Neither follows.

    Second statement states that All Singers are Intelligent which means some intelligent people are singers.

    it does not mention that all singers have to be intelligent so in that context we can conclude that some intelligent people are not singers so conclusion 2 can be inferred.

    But as per the rules we get answer 4 UP + PP === no conclusion.

    I don’t think the rules apply well here.

    • Shivraj says:

      Small correction:

      **** it does not mention that all intelligent people have to be singers ***

  29. RAVI NAMDEV says:

    REALLY ITS AMAZING EXPLANATION OF SYLLOGISM IT’S VERY HELPFUL FOR ME TO CRACKING SSC EXAM THANKS A LOT DEAR I HAVE ALREADY CRACK CGL SSC 2013 AND NCB AS WELL AS INTELLIGENCE BUREAU THANKS A LOT FOR GIVING SUCH TYPE HELP

  30. nitesh says:

    please solve this

    Statement: I. All fish are tortoise.
    II. No tortoise is a crocodile.
    Conclusions: I. All tortoise is a fish.
    II. No fish is a crocodile.

  31. avnish urmaliya says:

    Thanks sir

  32. hmt says:

    Mrunal sir everything is clear except possibility case.
    For example:
    Statement: Some mail are chats.
    All updates are chats.
    Conclusion:All mails being update is a possibility.
    No update is a mail.
    1) 1 follows.
    2) 2 follows
    3) neither 1 nor 2
    4) either 1 or 2
    5) both follows.

    One more concept on Possibility case would be great.
    Thanks in advance.(I don’t wanna use VEN no more.)

  33. yd.maurya says:

    sir, plz provide venn diagram method

  34. barkha chadha says:

    sir, this is awesome,, till now i had thought it is just to be understood in language terms…..and grammar….but i was wrong,,,,this is to be done using logical steps like maths….gained confidence….thankyou for clearing all doubts and teaching in such a good analytical way….may god bless u and keep up the gud job…
    barkha

  35. barkha chadha says:

    sir, pl give explanation for this question
    all boys are rivers,
    some rivers are girls.
    A) some girls may be boys
    b) some boys may be girls
    options:
    1)only a follows
    2) only b follows
    3) both a /b follows
    4) neither a nor b follows

    my ans coming as 4th option …pl clarify

  36. barkha chadha says:

    pls solve these for me as my answeres coming wrong

    some aeroplanes are cars. some cars are carts, so
    1) some carts are aeroplanes
    2) some carts are not cars.

    1) if only a follows
    2) if only b follows
    3) if both follows
    4 if neither follows

    q2) some workers are leaders. all leaders are poor. therefore
    1) some workers are poor
    2) some workers are not poor.

    q3) all wathes are crowbars. all crowbars are bricks. therefore
    1) all bricks are crowbars
    2) some bricks are crowbars.

  37. barkha chadha says:

    pl clarify this que
    1) some dead are ghost(pp), all ghosts are angels
    conclusions
    1 some dead are angels
    2 some dead are not ghosts
    3 all deads are either angels or ghosts
    4 all angels are ghosts

    1 only 1 and 2 follow
    2 only 2 n 3
    3 either 3 or 4
    4 only 3 follows………….my ans is that only one statement some dead are angels is correct…what am i doing wrong

    • ashok says:

      u r right .

      • barkha chadha says:

        thanx for replying ashok but it says that ans is option 1 i.e only 1 and 2 follows how?

  38. sudevan chib says:

    All oranges are apples.Some apples are bananas.Only mangoes are apples
    conclusion
    At least some oranges are bananas
    All oranges are mangoes

    can you please explain me this question with the help of venn diagram and notify me through email

  39. navaneethan says:

    can i use arun sharma books for sbi po?

  40. Seema says:

    Hi All,

    I am not getting this special conversion rule here.
    can you please provide some explanation for this.
    It will be of great help.

    Thank you !!

  41. Apurv says:

    Thanks a lot Sir!!! You expained it very well. Now I feel confident about solving these type of questions.

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