syllogism high level

[Reasoning] 4-Statement Syllogism: Approach, Techniques, explained for SBI

PO (High level reasoning) and UPSC CSAT paper 2

1. Introduction2. Recap: 2 statement3. Complimentary case

4. Approaching 4 statement syllogism5. Case#1 : Stick, lamps, power, dresses, shirts

6. Case#2: Bird, Horse, Tiger, Lion & Monkey7. 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 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 terms2. 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

1. Universal Positive (UP)

2. All cats(A) are dogs (B)

Only PP Some Cats (A) are dogs.

(B) Some dogs (B) are cats.

(A)

1. A to B2. B to A

3. Universal Negative (UN)

4. No Cats(A) are dogs (B)

PN :Some Dogs (B) are not Cats (A).

B to A UN: No Dogs (B) are

cats. (A)

5. Particular Positive (PP)

6. Some cats (A) are dogs (B)

Only PP: Some dogs (B) are cats(A) B to A

7. 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

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

1. Some Politicians are honest.

2. No Politicians are honest

1. Some Politicians are honest.2. 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)

1. All Politicians are honest.2. Some Politicians arenot

honest

PP + Pritish Nandy (PN)

1. Some Politicians are honest2. 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.” (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

a. None followsb. Only 1c. Only 2d. Only 3e. 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

a. Only 1 and 3b. Only 1, 2 and 3c. Only 2, 3 and 4

d. Only 1, 2, 3 and 4e. 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)


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.


2 Some Monkeys are Birds PP

If this is valid, who’re its parents?





I’ll reorder so it makes more sense





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

a. Only 1 and 3

b. Only 1, 2 and 3c. Only 2, 3 and 4

d. Only 1, 2, 3 and 4e. None follows

Final answer (A) Only 1 and 3 follow.

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


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

a. Only 1 and 2b. Only 1 and 3c. Only 3 and 4

d. Only 2, 3 and 4e. 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


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:



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)?


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



Final answer: C, only 3 and 4 follows.

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


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

a. Only 1 followsb. Only 2c. Only 3d. Only 4

e. Either 1 or 3 follows.

Approach

Let’s start with conclusion 1.


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


3 No Table is Bottle UN

Apply the checklist for complimentary case.

a. Two answer choices have same subject and predicate?= YES

b. The answer choice combo must be either of these three

i. Uttar Pradesh (UP) + Pritish Nandy (PN)ii. PP + Pritish Nandy (PN)

iii. 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

a. Only 1,2,3 followb. Only 2,3 and 4 follow

c. Either 1 or 3 AND 2 followd. Either 1 or 3 AND 4 follow

e. 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:




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




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.

syllogism high level

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