# 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.

 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. 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. 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.

# 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.

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.”

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

## 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 Some Honest men are not Politicians. Particular negative (PN), hence eliminate. No Honest men are politicians. Universal Negative, hence eliminate Some Honest men are politicians. PP hence this is correct answer. 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) Sardar Patel Lal Bahadur Shastri Raja Kalmadi Predicate (Honest Men) Sardar Patel 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

• 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”.
For the moment, let’s not complicate the matters with complimentary pairs.

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 UP+UP=UP If Uttar Pradesh meets Uttar Pradesh, then its size doesn’t increase. UP+UN=UN If Uttar Pradesh meets United Nations then its size increases and it becomes United Nations. 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) 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

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.

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

Third step, classify the statements.

 All men are women. Universal Positive (UP) 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)

 All Men are crazy Correct. 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! Some of the crazy are men Correct because of “conversion table” 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

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.

 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.

# 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

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.

# DemoQ: Working mother nurses (CAT)

 question statement answer choices No mother is a nurse. Some Nurses like to work No woman is prude Some prude are also nurses Some nurses are women All women like to work ABE CED FEB 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.

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).

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 All honest(people) are politicians UP No non-politician is honest. No honest (people) are non-politicians. UN 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.

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

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

## Case#2

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 All women(B) are birds Some women(B) are tree Some birds are tree 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 Some birds(A) are women (B) 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 All women(B) are birds Some women(B) are tree Convert second statement. (PP to PP) All women(B) are birds. Some trees are women(B). Now exchange positions of question statements Some trees are women(B). (PP) 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 All the flowers are leaves.(B) (UP) Some leaves(B) are birds (PP) Some birds are flowers 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 Some birds are flowers Not possible because combo rule. 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.

## 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.

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

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

1. 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+?

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

2. 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???

1. 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.

1. 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.

2. 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.

2. 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.

1. 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

3. 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.

1. Any solution for this problem

4. 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

5. well explained. thanx

6. 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

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

1. ans c

9. 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

10. 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

1. sorry typing mistake….

correct S2 is

S2 :shobha is very fair

11. 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)

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???????????/

1. Hello Sir,
pg 7 R s agarwal

S 1: All students in my class are intelligent(UP)
S 2: Rohit is not intelligent(UN)

C 1: Rohit is not a student of my class
C 2: Rohit must work hard

Acc. to priority order UN should be followed by UP,
and for std. format UP is converted to PP.
and it goes like
S1 : Rohit is not intelligent(UN)
S 2: SOME INTELLIGENT ARE STUDENTS OF MY CLASS (PP)

now, acc to you
UN + PP = PN(C->A) , so it must be like so SOME STUDENT OF MY CLASS ARE NOT ROHIT.
so finally i got wrong myself, where am i commiting mistake, if not what is answer,
PLS HELP ME.

12. 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

1. 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

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

14. 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

1. Dear Palanisamy,

Plz tell me about tick Method of solving syllogism questions

15. 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

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

17. 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)

18. Question Statements (SSC-CPO exam)

All poets are intelligent
All singers are intelligent.

Conclusion

all singers are poets
some intelligent persons are not singers

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.

1. Small correction:

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

19. 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

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.

1. simple All + no = no
No fish is crocodile should be the answer

21. Thanks sir

22. Mrunal sir everything is clear except possibility case.
For example:
Statement: Some mail 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.)

1. Same prob???

1. Hey HMT, Do u find any solution?

23. sir, plz provide venn diagram method

24. 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

25. 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

26. 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

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.

1. Q1: 4, Q2: 1, Q3: 2…
post the ans in comment and the source of ques…
some books hav wrong ans on some ques…

27. pl clarify this que
1) some dead are ghost(pp), all ghosts are angels
conclusions
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

1. u r right .

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

1. r u sure thr is no 5th option like None of these…?
can u plz send the link of source of ur question…
dont take it otherwisw bcoz in po ques thr r 5 options…

28. 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

29. can i use arun sharma books for sbi po?

30. 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 !!

1. 3 things

All s is p is equal to some p is s which is equal to some s is p.
some s is p is equal to some p is s.
and no s is p is equal to no s is p and which is equal to some p are not s.

Plz check venn diagram for more clarifications