[Reasoning] 4-Statement Syllogism: Approach, Techniques, explained for SBI PO (High level reasoning) and UPSC CSAT paper 2 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 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 1. Universal Positive (UP) 2. All cats(A) are dogs (B)
3. Universal Negative (UN) 4. No Cats(A) are dogs (B) 5. Particular Positive (PP) 6. Some cats (A) are dogs (B) 7. Particular Negative (PN)
Valid Conversion Only PP Some Cats (A) are dogs. (B) Some dogs (B) are cats. (A)
Path
PN :Some Dogs (B) are not Cats (A).
1. A to B 2. B to A
UN: No Dogs (B) are cats. (A)
B to A
Only PP: Some dogs (B) are cats(A)
B to A
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 1. Some Politicians are honest.
Not applicable 1. Some Politicians are honest.
2. No Politicians are honest
2. No Honest are Politicians.
Because both have common In first statement, subject=Politician but in subject (politician) and second statement, subject= Honest. common predicate (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 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.” (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 4statement 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
4
4. all
dresses are
PP
shirts
UP
sticks
PP
conclusion statements 1
some
shirts are
2
some
shirts are flowers
3
some
flowers are
sticks
PP
4
some
dresses are
sticks
PP
PP
Answer choice a. None follows b. Only 1 c. Only 2 d. Only 3 e. 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 1
All
2
all
3 4
Birds
predicate Type are Horses
UP
Horses are
Tigers
UP
Some
Tigers
are
Lions
PP
Some
Lions
are Monkeys PP
conclusion statements 1
Some
2
Some
3
Some
4
Some
Tigers
are Horses
Monkeys are Tigers
are
PP
Birds
PP
Birds
PP
Monkeys are Horses
PP
Answer choice a. Only 1 and 3 b. Only 1, 2 and 3 c. Only 2, 3 and 4 d. Only 1, 2, 3 and 4 e. 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
2
all
Birds are Horses UP 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
Tigers
UP
1
All
Horses are
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 a. Only 1 and 3
b. Only 1, 2 and 3 c. Only 2, 3 and 4 d. Only 1, 2, 3 and 4 e. None follows Final answer (A) Only 1 and 3 follow.
Case#3: Bench, Wall, House, Jungle, Road Question statement Subject 1
Some
2
All
3
Some
4
All
predicate Type
Bench Are
Wall
PP
House
UP
House Are Jungle
PP
jungle Are
UP
Wall
Are
Road
Conclusion Statements 1
some
Roads Are Benches PP
2
Some
Jungles Are
3
Some
Houses Are Benches PP
4
some
Roads Are Houses
Walls
PP PP
Answer choices a. Only 1 and 2 b. Only 1 and 3 c. Only 3 and 4 d. Only 2, 3 and 4 e. 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:
a. Only 1 and 2 b. Only 1 and 3 c. Only 3 and 4 d. Only 2, 3 and 4 e. 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 a. Only 1 and 2 b. Only 1 and 3 c. Only 3 and 4 d. Only 2, 3 and 4 e. None follows. Final answer: C, only 3 and 4 follows.
Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables Question statement Subject 1
All
2
Some
3
No
4
some
predicate Type
Cups are Bottles Bottles are Jug
is
Plates are
UP
Jugs
PP
Plate
UN
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 follows b. Only 2 c. Only 3 d. Only 4 e. 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
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.
Tables_D PP
Subject
Predicate
1 Some Tables are
Bottles
PP
3
Bottle
UN
No
Table
is
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 1. Some 2. All
chairs
Type
are Handles PP
Handles are
Pots
UP
Mats
UP
3. All
Pots
are
4. Some
Mats
are Buses
PP
Conclusion Statement 1. Some
buses
are handles PP
2. Some
mats
are chairs
3. No
bus
4. Some
mats
is
handle
PP UN
are handles PP Answer choices
a. Only 1,2,3 follow b. Only 2,3 and 4 follow c. Either 1 or 3 AND 2 follow d. 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: a. Only 1,2,3 follow b. Only 2,3 and 4 follow c. Either 1 or 3 AND 2 follow d. Either 1 or 3 AND 4 follow e. 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 3. all
Handles(B) are Pots(C)
are
Pots(C)
UP
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 a. Only 1,2,3 follow b. Only 2,3 and 4 follow c. Either 1 or 3 AND 2 follow d. Either 1 or 3 AND 4 follow e. 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.
