# Introduction

• SBI loves asking 4 statement syllogism questions in its PO exam. (usually 5 questions.)
• In 2012, UPSC asked 3 statement syllogism in CSAT paper II, and nothing prevents UPSC from asking 4-statement syllogism in future, under its BackbreakingTM move.
• Therefore, anyone who doesn’t want to dig his/her grave in SBI or UPSC, should thoroughly prepare syllogism.
• Good news is, no matter whether they ask 2 statement syllogism, 3 statement syllogism, 4 statement syllogism or 50 statement syllogism, our UP-UN method continues to work.
• However, to quickly and accurately solved 4 statement syllogism, first you must master earlier techniques
 Two statement syllogism Click me to learn Three statement syllogism Click me to learn

# Recap: 2 statement

Whenever facing two statement syllogism, our standard operating procedure is:

1. Two statements, must have only three terms
2. Classify them into UP, UN, PP or PN.
3. Two statements must be in the Format A to B then B to C, if not then apply the conversion rules
 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. –
1. Now apply the combo rules. Unless specifically mentioned, conversion is A to C.

## Yes 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. (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)

# Complimentary case

• Incase you get a no-conclusion combo, BUT any of the answer choice says “either ** or ** follows.” In that case you’ve to check for complimentary cases. (this is critical for SBI PO, since often the 4 statement conclusion have complimentary case situation).
• For complimentary case to be valid, two conditions must be met:

Condition #1: Two answer choices have same subject and predicate.

 Applicable Not applicable Some Politicians are honest. No Politicians are honest Some Politicians are honest. No Honest are Politicians. Because both have common subject (politician) and common predicate (honest) In first statement, subject=Politician but in second statement, subject= Honest. Hence complemantary case not possible.

Condition#2:  The answer choice combo must be either of these three

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

When these two conditions are met, then answer would be “Either (I) or (II) follows.” (to see actual question related to the complimentary pair situation, check the case number 4 and 5 given in the later part of this article.)

# Approaching 4 statement syllogism

• Here you pick up conclusion one at a time, find its parents.
• Apply chain formula and see if it leads to the given conclusion. (pretty much the same thing that we do in three statement syllogism click me)
• Anyways without much ado, let’s start solving 4-statement syllogism questions from SBI PO 2010 exam

# Case#1 : Stick, lamps, power, dresses, shirts

This is a really cheap and easy question.

 Question statements Subject predicate Type 1 1. some sticks are lamps PP 2 2. some flowers are lamps PP 3 3. some lamps are dresses PP 4 4. all dresses are shirts UP conclusion statements 1 some shirts are sticks PP 2 some shirts are flowers PP 3 some flowers are sticks PP 4 some dresses are sticks PP

1. None follows
2. Only 1
3. Only 2
4. Only 3
5. Only 4.

## Approach

• You can start with one conclusion at a time, find its parents and then apply combo rules.
• But if you look at it carefully: 3 out of 4 question statements are Particular Positive (PP). So if you pick any two of them, PP+PP=no conclusion.
• Fourth question statement is UP.  UP+PP=PP if this is intermediate conclusion, it won’t give any final conclusion when paired with any other question statement because PP + PP = no conclusion.
• If situation requires you to convert UP (=can only be converted into PP), then again PP+PP=no conclusion.
• So with that thought in mind, check four conclusion statement, you’ll see none of their parents can give conclusion.
• Therefore answer is (A) none follow.

# Case#2: Bird, Horse, Tiger, Lion & Monkey

 Question statement Subject predicate Type 1 All Birds are Horses UP 2 all Horses are Tigers UP 3 Some Tigers are Lions PP 4 Some Lions are Monkeys PP conclusion statements 1 Some Tigers are Horses PP 2 Some Monkeys are Birds PP 3 Some Tigers are Birds PP 4 Some Monkeys are Horses PP

1. Only 1 and 3
2. Only 1, 2 and 3
3. Only 2, 3 and 4
4. Only 1, 2, 3 and 4
5. None follows.

## Approach

• As you can see conclusion #3 is reappearing in option A to D. so first I’ll check conclusion #3. If it turns out to be false then my effort is saved, I’ll directly tick (E).

## Checking conclusion #3

 3 Some Tigers are Birds PP

If this conclusion is valid, who’re its parents?

 1 All Birds_A are Horses_B UP 2 all Horses_B are Tigers_C UP
• Ok this is in standard format: A to B then B to C.
• Apply combo rule: when UP is merged in UP, its size doesn’t increase (UP+UP=UP, A to C). so my conclusion is All birds_A are tigers_C. I’ll reconvert this (UP to PP), so some tigers are birds. This matches with the conclusion number #3.
• So conclusion #3 is valid. So option E is eliminated.
• Now I’ll have to check other conclusions as well. Anyways, now let’s check all other conclusions in serial order (1, 2, 4)

## Checking conclusion #1

 Concl.1 Some Tigers are Horses PP

If this is legit, who’re its parents?

Just one:

 Q.Statement 2 all Horses are Tigers UP

I can convert this! (UP to PP) so some tigers are horses. So conclusion #1=valid.

## Checking conclusion #2

 2 Some Monkeys are Birds PP

If this is valid, who’re its parents?

 1 All Birds are Horses UP 2 all Horses are Tigers UP 3 Some Tigers are Lions PP 4 Some Lions are Monkeys PP

I’ll reorder so it makes more sense

 4 Some Lions are Monkeys PP 3 Some Tigers are Lions PP 2 all Horses are Tigers UP 1 All Birds are Horses UP
• Ok we are facing 4 statement chain. We’ve to pick two at a time get intermediate conclusions, pair them with next statement and keep moving.
• But today is my lucky day, you see first two statements are PP + PP= no conclusion. So we can’t proceed further. And answer choice doesn’t contain any “either or”. So we don’t need to check complimentary case either. That means conclusion #2 is invalid. Our precious time and effort is saved.

So far we’ve done following

 Conclusion number Valid/not? 3 Valid 1 Valid 2 Invalid.

1. Only 1 and 3
2. Only 1, 2 and 3
3. Only 2, 3 and 4
4. Only 1, 2, 3 and 4
5. None follows

Final answer (A) Only 1 and 3 follow.

# Case#3: Bench, Wall, House, Jungle, Road

 Question statement Subject predicate Type 1 Some Bench Are Wall PP 2 All Wall Are House UP 3 Some House Are Jungle PP 4 All jungle Are Road UP Conclusion Statements 1 some Roads Are Benches PP 2 Some Jungles Are Walls PP 3 Some Houses Are Benches PP 4 some Roads Are Houses PP

1. Only 1 and 2
2. Only 1 and 3
3. Only 3 and 4
4. Only 2, 3 and 4
5. None follows.

## Approach

To save time and effort, I am going to test only 2 and 4. Let’s see if I can get lucky!

## Checking conclusion statement #2

 2 Some Jungle Are Wall PP

If this is valid conclusion, who’re its parents (question statements)?

 2 All Wall Are House UP 3 Some House Are Jungle PP
• Cool, already in standard format A to B then B to C.
• And UP’s politicians hate giving particular statements so UP+PP=no conclusion.
• So conclusion #2 is invalid, that means answer choice A and D are eliminated. Let’s see what is left in the answer choices:
1. Only 1 and 2
2. Only 1 and 3
3. Only 3 and 4
4. Only 2, 3 and 4
5. None follows.

Ok now let’s check conclusion #4.

## Checking conclusion statement #4

 4 some Roads Are Houses PP

If this is valid conclusion, who are its parents (question statements)?

 3 Some House Are Jungle PP 4 All jungle Are Road UP
• Good, already in standard format: A to B then B to C. so directly apply the combo rule.
• 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)
• PP+UP=PP. (A to C)
• Therefore my conclusion is Some Houses are roads. And PP can be converted into PP. So Some roads are houses = also valid.
• So conclusion #4 is valid. Let’s check our answer choices
1. Only 1 and 2
2. Only 1 and 3
3. Only 3 and 4
4. Only 2, 3 and 4
5. None follows.

Final answer: C, only 3 and 4 follows.

# Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables

 Question statement Subject predicate Type 1 All Cups are Bottles UP 2 Some Bottles are Jugs PP 3 No Jug is Plate UN 4 some Plates are tables PP Conclusion Statements 1 Some Tables are Bottles PP 2 Some Plates are Cups PP 3 No Table is Bottle UN 4 Some jugs are cups PP

1. Only 1 follows
2. Only 2
3. Only 3
4. Only 4
5. Either 1 or 3 follows.

## Approach

 1 Some Tables are Bottles PP

If conclusion 1 is valid then who’re its parents (question statements)?

 2 Some Bottles are Jugs PP 3 No Jug is Plate UN 4 some Plates are tables PP

I’ll rearrange the order

 2 Some Bottles_A are Jugs_B PP 3 No Jug_B Is Plate_C UN 4 some Plates_C are Tables_D PP
• Now it is a three statement syllogism.
• Already in standard format. So, First combine 2+3.
• PP+UN=PN. (A to C)
• Some Bottles_A are not plates_C.  (PN)
• That’s my intermediate conclusion. Now I’ll combine it with question statement number 4.
 Intermediate conclusion Some Bottles_A Are not Plate_C PN Q. statement #4 some Plates_C are Tables_D PP
• Two particulars = no conclusion.
• Ok so, conclusion #1=cannot be concluded definitely.
• But wait, look at answer choice #4: either 1 or 3 follows. So this could be a case of complimentary pairs.
• Let’s relook at conclusion statement #1 and #3.
 Subject Predicate 1 Some Tables are Bottles PP 3 No Table is Bottle UN

Apply the checklist for complimentary case.

1. Two answer choices have same subject and predicate?= YES
2. The answer choice combo must be either of these three
1. Uttar Pradesh (UP) + Pritish Nandy (PN)
2. PP + Pritish Nandy (PN)
3. PP + United Nations (UN)

Yes, it is combo number III (PP+UN). So final answer is either 1 or 3 follows.

# Case#5: (Complimentary Pairs): Chair, Handle, Pots, Mats & Buses

 Question statements are Type 1. Some chairs are Handles PP 2. All Handles are Pots UP 3. All Pots are Mats UP 4. Some Mats are Buses PP Conclusion Statement 1. Some buses are handles PP 2. Some mats are chairs PP 3. No bus is handle UN 4. Some mats are handles PP

1. Only 1,2,3 follow
2. Only 2,3 and 4 follow
3. Either 1 or 3 AND 2 follow
4. Either 1 or 3 AND 4 follow
5. Either 1 or 3 AND 2 and 4 follow

## Approach

Take a look at c,d,e all of them contain “Either 1 or 3”. So we’ve to check for complimentary cases. Given conclusions

 1. some buses are handles pp 3. no buses is handle un
• Ok this both have some subject and predicate.
• And they’re in form of PP+UN. So, Yes, they’re fit for complimentary case= Either 1 or 3 follows. Let’s see our answer choices again:
1. Only 1,2,3 follow
2. Only 2,3 and 4 follow
3. Either 1 or 3 AND 2 follow
4. Either 1 or 3 AND 4 follow
5. Either 1 or 3 AND 2 and 4 follow
• C says “either 1 or 3 AND 2”
• We have already checked that either 1 or 3 is valid.
• Now let’s test conclusion statement number 2
 2. some Mats Are chairs PP

If this is valid then who’re its parents (question statements)?

 1. some Chairs(A) are Handles(B) PP 2. all Handles(B) are Pots(C) UP 3. all Pots(C) are Mats(D) UP

Ok now let’s pair up 1 and 2

 1. some Chairs(A) Are Handles(B) PP 2. all Handles(B) Are Pots(C) UP
• Are they in standard format A to B B to C? yes.
• Apply rules. PP + UP.
• 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)
• Therefore, PP + UP = PP (A to C)
• Intermediate Conclusion statement is Some chairs(A) are pots(C)
• Combine intermediate conclusion with q.statement #3.
 Some chairs(A) are pots(C) PP 3. all Pots(C) are Mats(D) UP
• Are they in std. format? yes they’re in standard format, (A to C C to D)
• Apply rules. PP + UP = PP (A to D).
• Our conclusion: Some chairs (A) are mats(D)==>convert Some mats are chairs (PP to PP).
• Conclusion statement #2 said: some mats are chairs.
• Yes so conclusion statement #2 is legit. So far our situation is
1. Only 1,2,3 follow
2. Only 2,3 and 4 follow
3. Either 1 or 3 AND 2 follow
4. Either 1 or 3 AND 4 follow
5. Either 1 or 3 AND 2 and 4 follow
• Now let’s check conclusion statement #4.
 4.some mats are handles PP

Find its parents.

 2. all Handles_A Are Pots_B UP 3. all Pots_B are Mats_C UP
• 2+3= already in std format, UP+UP =UP merged with UP, size doesn’t hence.
• So UP+UP=UP (A to C) very easy. Conclusion will be All handles are mats (UP).
• But fourth conclusion is some mats are handles. No problem, we’ll convert our conclusion (rule UP–>PP).
• So, All handles are mats (UP) => Some mats are handles.
• Therefore, conclusion number 4 is also correct. Therefore Final answer: (e)  Either 1 or 3 AND 2 and 4 follow.

For more articles on reasoning and aptitude, visit Mrunal.org/aptitude

## Mrunal recommends

Books: UPSC Prelims Books: UPSC Mains Books: Maths /Reasoning

## 159 Comments on “[Reasoning] 4-Statement Syllogism: Approach, Techniques, explained for SBI PO (High level reasoning) and UPSC CSAT paper 2”

1. pls can anyone help me to understand syllogism by using venn diagram

:(

i did’nt get

2. gud one!!!

3. 1, 3, 4 are correct while 2 doesnt follow

4. very easy method thank u so much sir

5. Thanks a ton..!!! I always found 4 statement syllogisms very confused when combined with either or conclusions. But now let them give any number of statement, i am so confident to solve them all.. Thanks thanks thanksss,,,,!!! :)

6. Thanks for this and every article you have written, really you are doing a good job .
I have some problems in sylogism possibility questions ,can you write a post on that or guide me towards some book or link .

7. ur methods not working here..pls explain
all B are A
some C are A
all D are C
some E are B

conclusions:
1.some E are A
2.no B is D
3.some A are D

OPTIONS:
a) only 1 follows
b) 1 and 2 follows
c) 1 and either 2 or 3 follows
d)none follows

1. TO NEERAJ

ANS IS a) only 1st follows

1. option C
because we have either case here
which matches PP-UN case

1. No Ivan the basic condition that both subjects and predicates should be same is not followed. I agree with LUCKY.

8. hello sir
the method for syllogism are taken but i have little confusion in complementary pairs, will you please make it clear ASAP I HAVE MY EXAM ON 26th

9. can anyone tell me how to solve syllogism containing if and then plz…

Some symbols are figures .
All symbols are graphics.
No graphics is a picture.

conclusion
1 . Some graphics are figures.
2. No symbol is a picture .

1. Both 1 & 2 are true
From 1st & 2nd statements you can derive Conclusion 1 (PP-UP)
From 2nd & 3rd statements we have (UP-UN)

2. Only 2 follows

11. Some pencils are kites
Some kites are desks
All desks are jungles
All jungles are mountains

1.Some Mountains are pencils
2.Some jungles are pencils
3.Some mountains are desks.
4.Some jungles are kites.

(1)Only 1 and 3 follow
(2)Only 1, 2 and 3 follow
(3)Only 3 and 4 follow
(4)Only 2, 3 and 4 follow
(5)None of the above

I am getting answer Only 1 and 3 follow but the answer given is Only 3 and 4 follow.

12. Some pencils are kites
Some kites are desks
All desks are jungles
All jungles are mountains

1.Some Mountains are pencils
2.Some jungles are pencils
3.Some mountains are desks.
4.Some jungles are kites.

(1)Only 1 and 3 follow
(2)Only 1, 2 and 3 follow
(3)Only 3 and 4 follow
(4)Only 2, 3 and 4 follow
(5)None of the above

13. this method is comprehended by only mrunal.if you know 100-50 rule,plz eleborate

14. hello sir,
Thankyou for sharing this information… But could you please share the method for solving possibility case of syllogism…

15. Mrunal sir : plz find me the conlcusion of the following.

1.statement:

All ship can fly
all birds can fly

conclusion: most ships are birds.
2.statement :
most bags are heavy.
some packets are bag.
conclusion :
some packets may be heavy.
according to your table how could we treat “few” different with “most”….though you have mentioned that words like most ,few etc….are treated in “some” categoy.
plz explain the above two statement.

16. In each of the questions below are given three statements followed by two conclusions numbered I and II. You have to take the given statements to be ture even if they seem to be at variance with commonly known facts. Read all conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answer-

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

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

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

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

1. 1) only conclusion 2 follows..
2) both 1 and 2 follows..

17. Mrunal Sir,
Is there any article of yours in which you have explained about possibility type questions?
I make blunder in those questions!

18. Mrunal sir solve this cases of possibility plz
Statement:
1. all cats are dogs.
2. no dog is lion.
3. some lion are tigers.

Conclusion:
1. Some lions are cats is a possibility.
2. Some tigers are cat is a possibility.
3. All cats are tiger is not a possibility.
4. All tigers are dogs is not a possibility.

1. 2 conclusion follows

1. tell me if my method to solve possibility type questions is good or bad.

1) Using ‘lion’ and ‘cat’ we can write a definite conclusion. That conclusion is ” No lion is cat”. This is an Universal negative sentence. From an Universal negative statement No positive sentence is possible so conclusion 1 doesn’t follow

2) Using ‘tiger’ and ‘cat’ we can write a definite conclusion. That conclusion is ” Some tigers are not cats” which means either some tigers are cats or No tigers are cats. So there is a possibility that some tigers are cats hence conclusion 2 follows.

3) I have just told you that using ‘Tiger’ and ‘Cat’ the only conclusion we can deduct is “Some tigers are not cats”. The only impossible thing from this conclusion is ‘All tigers are cats’. All other statements like ‘ All cats are tigers’, ‘Some cats are tigers’, No cats are tigers and Some cats are not tigers are possible. So Conclusion 3 doesn’t follow

4) Using ‘tiger’ and ‘dog’ we can deduct a definite conclusion and that conclusion is ” Some tigers are not dog”. The only impossible thing from this conclusion is ” All tigers are dogs”. So conclusion 4 follows

1. HI,
2 & 4 conclusion follows.

2. 2 and 4 follow

19. Mrunal Syllogism and Deductions are same right? Or is there any diff b/w the 2?

1. More or less same.A syllogism is a three-part deductive argument. A deductive argument involves a chain of reasoning that leads to a necessary conclusion in light of given facts.(That is from a general premise to a specific conclusion)

1. ok thanks .. reason being the TIME material from where I am practicing theres no syllogism chap .. but deduction questions r there .. the questions for practice are 2 statement questions with 4 options .. I hope that will suffice .. if not any suggestions?

1. also refer to mrunal’s material regarding the same .Its comprehensive and sufficient for CSAT

20. mrunal sir..in case 4..cups bottles etc…pls check only 4..it follows..from statement 1 and statement 2.

21. PRITISH NANDY DOESN’T HATE EVERYBODY

I just want to tell an important thing. In lots of websites it’s given that when a Particular negative( O-type) sentence is one among in the two statements from which we have to deduct a conclusion, we cannot deduct a definite conclusion from both statements. I think that is wrong. It’s because I have personally analysed 64 combinations using the terms goats, dogs and cow with goat as middle term. Among in those 64 combination 28 combinations have particular negative sentence. In which, we cannot deduct a definite conclusion from 24 combinations. But we can deduct definite conclusion from 4 combinations which have particular negative sentence(O-type). Those 4 combinations are given below with conclusions

1. Statements: Some goats are not cow. All goats are dogs.

Conclusion we can deduct from these two statements is ” Some dogs are not cow”

2. Statements: Some cows are not goat. All dogs are goats.

Conclusion we can deduct from these statements is ” Some cows are not dogs”

3 Statements: Some goats are not dog. All goats are cows

Conclusion we can deduct from these statements is ” Some cows are not dogs”

4. Statements: Some dogs are not goat. All cows are goats

Conclusion we can deduct from these statements is ” some dogs are not cows”

22. Dear Mrunalji,
Kindly assist in explaining following question
a)No kite is slate
b)No jug is a slate
c)Some jugs are ropes
Conc:

i) Some ropes are slates
ii)Some ropes are not slates
iii) no kite is a jug
iv) some jugs are kites

A) either I or ii or iii follow
B) either iii or iv and ii follow
C) either I or ii and iii or iv follow
D) none

Regards

1. is it option 3? bdw conclusion 2 and 3 are correct… but acc to options… it seems like option C….plz reply ur ans…

23. 4. Statement:
Some rose are white.
All white which are rose are black.

Conclusion:
I. All roses is not black.
II. No white is rose.

(1) Only conclusion I follows
(2) Only conclusion II follows
(3) Either conclusion I or II follow
(4) Neither I nor II follow
(5) Both I and II follow

answer is -Neither I nor II follow
but am getting option firt as answer…
kindly help with this…
thnks

24. case 5 ?conclusion 2 ,how have u taken those parent statements…………………

25. Can anyone help me for

Statement 1 some rings are circles

Statement 2 no circle is a square

Conclusion 1 no ring is a square

2 all rings are squares

26. How to solve problems in which “possibility” is there, like
Statements:
Some teachers are professors.
Some lecturers are teachers.
Conclusions:
I. All teachers as well as professors being
lecturers is a possibility.
II. All those teachers who are lecturers are
also professors.
1) if only conclusion I follows.
2) if only conclusion II follows.
3) if either conclusion I or conclusion II follows.
4) if neither conclusion I nor conclusion II follows.
5) if both conclusions I and II follow.

27. Statements:
3. some questions are steps.
4. some inputs are steps.

Conclusion:

28. Statement:
1-All desks are chairs.

2-All chairs are tables.

3-All tables are boxes.

4-All boxes are trunks.

Conclusion:

I. Some trunks are tables.

II. All chairs are boxes.

III. Some boxes are desk.

IV. All desks are trunks.

only I and II follow
Only I, II and IV follow
Only II, III and IV follow
Only II, III and IV follow
All follow
None of these