1. Introduction
2. Recap: 2 statement
3. Complimentary case
4. Approaching 4 statement syllogism
5. Case#1 : Stick, lamps, power, dresses, shirts
6. Case#2: Bird, Horse, Tiger, Lion & Monkey
7. Case#3: Bench, Wall, House, Jungle, Road
8. Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables
9. Case#5: (Complimentary Pairs): Chair, Handle, Pots, Mats & Buses

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 Backbreaking^TM 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.	–

4. Now apply the combo rules. Unless specifically mentioned, conversion is A to C.

No conclusion combos

Yes conclusion combos

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) United Nations hates negativity. (both Universal and particular)(UN+UN/PN=NO) Pritish Nandy hates everybody. (first statement is PN=NO, Irrespective of second statement.) Two-negatives=no conclusion. Two particulars=no conclusion.

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

Answer choice

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

Answer choice

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.

Accordingly, Answer choice

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

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.

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

ANSWER choice

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

Approach

Let’s start with conclusion 1.

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

Answer choices

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

• So answer can be C/D/E. Let’s Start with answer choice C.
• 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.

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