- Introduction
- Recap: 2 statement
- Complimentary case
- Approaching 4 statement syllogism
- Case#1 : Stick, lamps, power, dresses, shirts
- Case#2: Bird, Horse, Tiger, Lion & Monkey
- Case#3: Bench, Wall, House, Jungle, Road
- Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables
- 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 doesnât 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
Recap: 2 statement
Whenever facing two statement syllogism, our standard operating procedure is:
- Two statements, must have only three terms
- Classify them into UP, UN, PP or PN.
- 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)
|
|
â |
- Now apply the combo rules. Unless specifically mentioned, conversion is A to C.
No conclusion combos
|
Yes conclusion combos
|
- UPâs 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 doesnât 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 âeither ** or ** follows.â In that case youâve 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: Â 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 âEither (I) or (II) follows.â (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, letâs 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
- None follows
- Only 1
- Only 2
- Only 3
- 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 wonât 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, youâll 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
- Only 1 and 3
- Only 1, 2 and 3
- Only 2, 3 and 4
- Only 1, 2, 3 and 4
- None follows.
Approach
- As you can see conclusion #3 is reappearing in option A to D. so first Iâll check conclusion #3. If it turns out to be false then my effort is saved, Iâll directly tick (E).
Checking conclusion #3
3 |
Some |
Tigers |
are |
Birds |
PP |
If this conclusion is valid, whoâre 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 doesnât increase (UP+UP=UP, A to C). so my conclusion is All birds_A are tigers_C. Iâll 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 Iâll have to check other conclusions as well. Anyways, now letâs check all other conclusions in serial order (1, 2, 4)
Checking conclusion #1
Concl.1 |
Some |
Tigers |
are |
Horses |
PP |
If this is legit, whoâre 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, whoâre 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 |
Iâll 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. Weâve 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 canât proceed further. And answer choice doesnât contain any âeither orâ. So we donât need to check complimentary case either. That means conclusion #2 is invalid. Our precious time and effort is saved.
So far weâve done following
Conclusion number |
Valid/not? |
3 |
Valid |
1 |
Valid |
2 |
Invalid. |
Accordingly, Answer choice
- Only 1 and 3
- Only 1, 2 and 3
- Only 2, 3 and 4
- Only 1, 2, 3 and 4
- 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
- Only 1 and 2
- Only 1 and 3
- Only 3 and 4
- Only 2, 3 and 4
- None follows.
Approach
To save time and effort, I am going to test only 2 and 4. Letâs see if I can get lucky!
Checking conclusion statement #2
2 |
Some |
Jungle |
Are |
Wall |
PP |
If this is valid conclusion, whoâre 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 UPâs politicians hate giving particular statements so UP+PP=no conclusion.
- So conclusion #2 is invalid, that means answer choice A and D are eliminated. Letâs see what is left in the answer choices:
- Only 1 and 2
- Only 1 and 3
- Only 3 and 4
- Only 2, 3 and 4
- None follows.
Ok now letâs 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. Letâs check our answer choices
- Only 1 and 2
- Only 1 and 3
- Only 3 and 4
- Only 2, 3 and 4
- 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
- Only 1 follows
- Only 2
- Only 3
- Only 4
- Either 1 or 3 follows.
Approach
Letâs start with conclusion 1.
1 |
Some |
Tables |
are |
Bottles |
PP |
If conclusion 1 is valid then whoâre its parents (question statements)?
2 |
Some |
Bottles |
are |
Jugs |
PP |
3 |
No |
Jug |
is |
Plate |
UN |
4 |
some |
Plates |
are |
tables |
PP |
Iâll 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. Â (PN)
- Thatâs my intermediate conclusion. Now Iâll 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.
- Letâs 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.
- Two answer choices have same subject and predicate?= YES
- The answer choice combo must be either of these three
- Uttar Pradesh (UP) + Pritish Nandy (PN)
- PP + Pritish Nandy (PN)
- 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
- Only 1,2,3 follow
- Only 2,3 and 4 follow
- Either 1 or 3 AND 2 follow
- Either 1 or 3 AND 4 follow
- Either 1 or 3 AND 2 and 4 follow
Approach
Take a look at c,d,e all of them contain âEither 1 or 3â. So weâve 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 theyâre in form of PP+UN. So, Yes, theyâre fit for complimentary case= Either 1 or 3 follows. Letâs see our answer choices again:
- Only 1,2,3 follow
- Only 2,3 and 4 follow
- Either 1 or 3 AND 2 follow
- Either 1 or 3 AND 4 follow
- Either 1 or 3 AND 2 and 4 follow
- So answer can be C/D/E. Letâs Start with answer choice C.
- C says âeither 1 or 3 AND 2â
- We have already checked that either 1 or 3 is valid.
- Now letâs test conclusion statement number 2
2. some |
Mats |
Are |
chairs |
PP |
If this is valid then whoâre 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 letâs 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 theyâre 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
- Only 1,2,3 follow
- Only 2,3 and 4 follow
- Either 1 or 3 AND 2 follow
- Either 1 or 3 AND 4 follow
- Either 1 or 3 AND 2 and 4 follow
- Now letâs 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 doesnât 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, weâll 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)Â Either 1 or 3 AND 2 and 4 follow.
For more articles on reasoning and aptitude, visit Mrunal.org/aptitude
Statements:
No chilli is potato.
No tomato is potato.
No tomato is apple.
Conclusions:
1. All chilli can be apple.
II. Some apple is not tomato.
III. Some potato is chilli is a possibility.
A. Both I and II
B. Both II and III
C. Only II
D. None of these
E. Only III