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

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  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-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 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 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.

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

Mrunal recommends

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

  1. usually one of the options is : either 1 or 2 follows
    This is usually given as answer when the conclusions are of the following types:
    1. some cats are dogs
    2. no cats are dogs

    but nobody considers that another option is possible which is ‘all cats are dogs’. So one of the three conclusions is possible not one of the two given above.
    So we can’t say ‘either 1 or 2 follows’ as a third conclusion can be written and answer shold be ‘one of the three follows’.

    1. @pk if no cats r dogs then hw all cats r dog? no cats are dogs mean no comon btwn cat and dog.hope m ryt. :)

  2. I want to ask about complementry conclusions, but according to venn diagram

  3. Sir thanku so much its true sense to help anybody whom u never know about them.

  4. I want to ask one syllogism question. Kindly give the answer.

    Statement: Some dogs bark.
    All dog bite.
    Conclusion:Those dogs who do not bark,also bite.
    Those dogs who do not bark,not neccessarily bite.

    1. Conclusion 1 follows . as All dogs necessarily bite.
      Biting to barking of dogs is not related anyways.
      Its necessary for all dogs.

  5. Hi mrunal,
    Thank you for sharing your knowledge with us.
    I have two doubts.
    Firstly, in the question: Statement: All men are women .All women are crazy.
    How is- ‘Some of the crazy are men’also a correct statement?
    None of the statements given in the question can be coneverted into this statement.
    and
    Secondly
    How to solve this question:
    Science teachers do not use plastic bags.
    Plastic bags are not used by some engineers.

    These subjects are directly given with no ‘All, Some’ etc words before them.

    1. stat: 1 all men(A) r women (B)
      2 all women(B) are crazy(C)
      first check statemnts hv three terms.? yes (men women and crazy)
      then is statements r in standard form? yes
      classify the statemnts 1 is UP nd 2 also UP
      then chek combo rules: no conclusion rules dsnt applicable ryt? now chek combo rule with yes conclusion
      in yes conclusion rules UP+UP=UP (A to C) which means from statemnts we get the result : ALL MEN ARE CRAZY this ansr is in UP form so we can cnvrt it into PP means SOME CRAZY ARE MEN which is also in conclusion. thats why this option also follow

  6. great work..bt i want about “WITH POSSIBILITY ” AND WITH OUT POSSIBILITY “” CASES PLS EXPLAIN….

  7. if there are three conclusions
    1 some cakes r not frogs
    2 some cakes r frog
    3 all frogs are cakes
    i knw accrding to quest my secnd conc is ryt . is it possible if all frog r cakes is wrong conc then according to secnd conc. 1 conc is true.???

    1. Hii Killer Miller,
      I think all three conclusions are true.

      Draw a vein diagram in which cake is big circle and, frogs and not frogs are subset circles without overlapping.

      Hope you get your answer..

  8. hi, I have the same doubt . please help. in RS Agarwal’s book it is stated that “even if it a statement with conclusion, we have to check for complementary pairs ” , which is contrary to what mrunal sir said. somebody please help.

    1. same doubt..did you get answer??

  9. Statements: All flowers are trees. No fruit is tree.
    Conclusions:No fruit is flower.
    Some trees are flowers.
    A. Only conclusion I follows
    B. Only conclusion II follows
    C. Either I or II follows
    D. Neither I nor II follows
    E. Both I and II follow

    answer is E.how?

  10. statment-
    1.only writers are poet
    2.many poet are singer
    3.many singer are actor
    4.no singer is a dancer
    conclusion-
    1.some writers are singer
    2.some actors are not dancers

  11. Hi, I had a doubt regarding complimentary pairs. Complimentary pairs are represented using either. And by either or we mean contradictory statements. But only NO & SOME(UN&PP) and ALL & SOME NOT(UP & PN) are contradictory. And SOME and SOME NOT are sub-contrary. Then how can they be a complimentary pair .

  12. Sir please assist in this question.
    Statements:
    All games are shames.
    Some shames are names.
    Conclusions;
    1. Some games are names.
    2. No game is a name.
    options;
    1.if only 1 follows
    2. if only 2 follows
    3. if either 1 or 2 follows.
    4. if neither 1 or 2 follows.
    5. if both 1 and 2 follows.

    1. all games are shames. (UP)
      some shames are names.(pp)
      so using UP+PP=No conclusion
      conclusion
      1. some games are names.(PP)
      don’t follow
      2.No game is a names.(UN)
      don’t follow
      So ans should be neither of 1 or 2 followS
      we can also check for either but as you said either is NT POSSIBLE IN UP+PP.
      BUT THE CORRECT ANS IS EITHER 1 OR 2 FOLLOWS HOW IS IT POSSIBLE. PLEASE HELP ME. THANK YOU.

  13. please explain me 3 statements and possibilities.. please sir

  14. Among the following statements two are contradictory to each other.select the correct code that represents them
    statements
    a. All poets are philosophers
    b.some poets are philosophers
    c.some poets are not philosophers
    d.no philosopher is a poet
    code:
    a&b
    a&d
    a&c
    b&c

  15. all dinosaurs are prehistoric creatures. Water buffaloes are not dinosaurs. Water buffaloes are not prehistoric creatures.

    UP+UN=UN
    This should be correct ?

  16. where can i find 3 statements syllogisms as you said that it will be in seperate article

  17. All men are tall. Those who are tall are thin.
    Conclusions: I. All men are thin. II. Some men are fat.
    sir kindly solve this this problem. i have read thoroughly the tips and tricks u have provided to solve problem related to syllogisms. i am getting some different answer using your tips which do not match with your formula.

    1. Answer : UP + UP=UP ( All men are thin )

  18. Statement 1 : Some huts are mansions
    Statement 2 : No mansion is a palace

    Conclusion 1 : All palaces being huts is a possibility
    Conclusion 2 : All huts are palaces

    I feel the answer should be Neither 1 nor 2 as PP+UN=PN ( NASA Telescope) i.e Some huts are not palaces .

    But I see in 2 of the sources that the answer is “Only Conclusion 1 follows” which is strangely a UP :D .

  19. Hi Naz,

    Stmt:
    1. All children are naggers [UP]
    2. Some children are whiners [PP]

    Conclusion:
    a. No naggers are whiners
    b. All naggers are whiners
    c. Some naggers are whiners
    d. None of the above

    Solution:
    As per the priority order [PP>UN>UP]
    U should convert the second statement.

    ie. Convert ,
    ‘Some children are whiners’ [PP] to
    Some whiners are children

    After conversion the statements are,

    1. All children are naggers
    2. Some whiners are children

    Now, the statements are not in the standard format. Therefore interchange the positions of the statements.

    ie.
    1. Some whiners are children [PP]
    2. All children are naggers [UP]

    By rule, PP+UP=PP

    Hence ‘some naggers are whiners’ [PP]

  20. Great work sir. Keep it up!

  21. Hello sir
    Statements: Some mangoes are yellow. Some tixo are mangoes.

    Conclusions:

    Some mangoes are green.
    Tixo is a yellow.
    A. Only (1) conclusion follows
    B. Only (2) conclusion follows
    C. Either (1) or (2) follows
    D. Neither (1) nor (2) follows
    E. Both (1) and (2) follow
    sir in this question pp+pp =no conclusion a/q the rules.
    then after a/q to rules we have to check if either 1 or 2 follows a/q to rules then i have checked no subject and predicate are same neither complementary pairs are same..then i should change a/q to priority order then sir if both are of pp which to change first ….confused.
    plss help reply soon

    1. There are 4 terms so no conclusion

  22. Statements: Some papers are pens. All the pencils are pens.

    Conclusions:

    Some pens are pencils.
    Some pens are papers.
    A. Only (1) conclusion follows
    B. Only (2) conclusion follows
    C. Either (1) or (2) follows
    D. Neither (1) nor (2) follows
    E. Both (1) and (2) follow
    pls explain

      1. It should be ‘B’ as the first statement can be rewritten as 2nd conclusion, PP = PP, single statement problem.

    1. E. As both conclusions are converse of both statements, therefore they both follow

    2. if we go by the rules above it should be D..

    3. ANS: E

      Explanation.
      1.Some papers are pens. – PP
      2.All the pencils are pens.- UP
      not in order so we have to do conversion .. as per the conversion priority , need to convert pp first.
      1.Some pens are papers
      2.all the pencils are pens.
      Now just interchange both statements.
      1.all the pencils are pens. -UP
      2.Some pens are papers -PP
      UP+PP – No Conclusion.
      But observe the conclusions carefully.
      Some pens are pencils(PP) which we can derive from 1.all the pencils are pens. -UP–>PP(B to A) so correct.
      Some pens are papers(PP) which we can derive from 2. Some pens are papers (PP–>PP) B to A so correct.
      so final answer is E.

    4. pp+up=pp
      some pens are pencils
      some papers are pens

      some pens are papers&some some pens are papers,so both 1& 2 follow

  23. Statements:
    Some books are toys.
    No toy is red.
    Conclusions:
    1. Some toys are books.
    2. Some books are not red.
    explain

    1. 2
      PP+UN= PN

  24. please tell the method of solving possibility cases asap??

  25. Sir,

    Thank you so much for this awesome method to approach syllogism (UP-UN method).

    I would like to request you to please tell me how to solve this type of syllogism:

    1. Statements: (A) Architects marry only fair girls. (B) Bimla is very fair.

    Conclusions: i) Bimla was married to an Architect. ii) Bimla was not married to an architect.

    2. Statements: (A) Sehwag is a good batsman. (B) Batsmen are physically powerful.

    Conclusions: i) All physically powerful are Batsmen. ii) Sehwag is physically powerful.

    1. 1) Either i or ii, i.e. complimentary pairs
      2) ii (UP+UP= UP)

      1. Both 1 and 2
        Is Sehwag Universal or Particular?

  26. Statement All A is B
    1 some B are A
    2 some A are B
    Which 1 or 2 follows statement
    Explain .

  27. Hello Sir,
    In the last section, I came across this question and it rattled my confidence of grasp.

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

    If I interchange the two statements vertically:

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

    (PP)+(UP)–>(PP)
    Conclusion given:
    Some birds are flowers (PP)
    Some leaves are flowers (PP)

    The conclusion I will be Reaching to is:
    Some flowers are birds (PP)
    We can Convert (PP) to (PP), so the above statement will be

    Some Birds are flowers.

    But the answer is the second option.
    Please help me, sir to understand where am I misunderstanding the concept.
    Regards

    1. answer is the second option only as if you draw ALL possible diagrams of the statements,the first conclusion won’t be true for all the diagrams.But it will be true in some diagram.Since The first conclusion is not true for all diagrams,therefore,some Birds are flowers is wrong.i follow Venn Diagram method

  28. Two questions
    1. Suppose if the statements are in the following format. B to A and C to B.. Is it okay to convert both the statements?

    2. But still am not getting the answer. Can you explain the following sum with this method.
    Statements: all film stars are singers. All film directors are film stars.
    Conclusions: all film directors are singers. Some film stars are film directors.

    1. Amongst the following statements, which would be logically compatible ?

      1. A shoe is a footwear.
      2. No sandal is a shoe.
      3. A shoe is a slipper.
      4. All footwear are shoes.
      5. A sandal is a footwear.

      a) 1,2,5
      b) 2,3,5
      c) 1,2,5
      d) 2,4,5

      Answer given is ‘C’. Can anyone explain this please ?

      1. Correction: the first option is : a) 1,2,3

    2. Both will follow.
      First Conclusion will directly follow from – All film directors are film stars. All Film Stars are Singers.
      Therefore All film directors are singers.

      Second conclusion is converse of second statement

  29. where can i find the possibiity cases of syllogism..i am not able to locate them..do they exist?

    1. same issue….some one please let us know how to solve possibilities using the above method…???????????

  30. Statement 1-All popular novels are best sellers
    Statement 2-Some literary novels are not best sellers
    Conclusion-Some literary novels are not popular

    Can You explain me the Solution sir/madam?

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