# [Reasoning] Three-Statement Syllogism: technique, method, shortcuts for IBPS, SSC, CSAT, CAT, CMAT

Don’t read further, until and unless you’ve mastered the 2-statement syllogism technique explained in previous article (click ME)

## Recap of 2-Statement syllogism

Before we understand the 3-statement syllogism, let’s recap the 2-statement trick just for refreshing your memory.
What to do when 2-statement syllogism question is given?

1. They must have only three terms (A, B and C)
2. Are the question statements in standard format (A to B then B to C)? if no, then refer to following conversion table. (important: priority order for conversion is PP>UN>UP.)
 Type Valid Conversion Universal Positive (UP) Only PP Universal Negative (UN) PN or UN Particular Positive (PP) Only PP Particular Negative (PN) Can’t do.

3. Classify the Question statement (UP, UN, PP, PN)
4. Apply the combo rules on Question statements.

## possible conclusion scenario

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)

5. (rarely required): if no-conclusion and “either or” given in answer, then check for Complimentary case.
Now we’ll see how to solve three-statement syllogism.

## Parent Statements

The crux of 2-statement syllogism was

1. When we’ve Question statements in standard format (A to B then B to C).
2. We apply some combo rules and may get a conclusion in the form of A to C

(or we may get the conclusion in form of “C to A”, in case the question statements were in the format of UN+(UP/PP). Recall the Ban-ki-Moon’s mood reversal).
In case of three statement syllogism, we accept the conclusion statement (A to C) as valid, then try to find out its parents (those question statements A to B then B to C).
Then, we try to get a valid conclusion out of those two-question statements and see if it matches with the given conclusion state in answer.
No need to get confused, let’s try with a simple scenario.

## conclusion statement

1. All cats are dogs
2. some pigs are cats.
3. All dogs are tigers
1. some tigers are cats
2. some pigs are tigers
3. all cats are tigers
4. some cats are not tigers

1. Only 1 and 2
2. Only 1, 2 and 3
3. All follow
4. None Follow

## i) Some tigers are cats (PP)

Q. if this is a valid conclusion, who’re its parents?
Ans. Thouse question statements with words “tigers”, “cats”, and a common term.
You can see, first and third statement fits the bill.

 Q.statement Type All cats(A) are dogs(B) UP All dogs(B) are tigers(C) UP
• Three terms=Ofcourse yes.
• Are they in standard format (A to B then B to C)? Yes.
• Then what are you waiting for? Just apply the combo rules. UP meets UP then its size doesn’t increase (UP+UP=UP) A to C. Hence conclusion will be “All cats are tigers.” (meaning given conclusion statement #3 is valid).
• If we convert this valid conclusion “All cats are tigers (UP)”, then UP–>PP= Some tigers are cats.

It means the given conclusion statement#1 is also valid.
So far: 1 and 3 are correct.
Now test the second conclusion statement.

## ii) some pigs are tigers

if this is a valid conclusion, who’re its parents?
Ans. . Thouse question statements with words “pigs”, “tigers”, and a common term(B).
But I don’t see any such question statements.
Now we’ll have to apply chain formula. Meaning, (A to B1, then B1 to B2, then B2 to C).
Consider this arrangement

 Question statements (CHAIN) Chain some pigs(A) are cats.(B1) Pig to Cat, cat to dog and finally dog to tiger. Let’s see if we connect pig to tiger. All cats(B1) are dogs(B2) All dogs(B2) are tigers(C)

We’ll take two statements at time and try to get an intermediate conclusion.

 Statement Type some pigs(A) are cats.(B1) Particular positive (PP) All cats(B1) are dogs(B2) Universal positive (UP)

Three terms = yes
Standard format= yes. (there A to B1 and then B1 to B2, which is just like A to B then B to C)
Apply combo-rule
PP+UP=PP (NASA mood change!) (A to B2)
Hence intermediate conclusion is Some pigs(A) are dogs(B2)
Now take this intermediate conclusion with the next statement in our chain.

 Question-statements Type Some pigs(A) are dogs(B2) Particular positive (PP) (derived) All dogs(B2) are tigers(C) Universal positive (UP) (given in question).

Again, same standard operating procedure of 2-statement syllogism.
Three terms = yes
Standard format= yes. (there A to B2 and then B2 to C, which is just like A to B then B to C)
Apply combo-rule
Again, PP+UP=PP (NASA mood change!) (A to C)
Therefore conclusion is Some pigs(A) are tigers (C).
Voila! Second conclusion statement is also correct.
So far 1, 2 and 3 are correct.
Let’s check the last statement (IV).

## iv) some cats are not tigers

while we were checking the first conclusion statement, we had found that “All cats are tigers (UP)”. Therefore, given conclusion statement is not possible.
Final answer: only 1, 2 and 3 are correct. (option b)

## DemoQ: Married Student Dancers (CSAT-2012)

Question statements

1. None but students are the members of the club.
2. Some members of the club are married.
3. All married persons are invited for dance.

Which one of the conclusions can be drawn from the above statements?

1. All students are invited for dance
2. All married students are invited for dance
3. All members of the club are married person
4. None of the above conclusions can be drawn

## Solution and approach

• first, rephrase the given statements so that processing becomes easier.
• Recall the “special conversion” rule from previous article on 2 statement.
• None but Politicians(A) are honest(B)=> All honest(B) are politicians(A) (Universal positive)
• I’m replacing the word “members of the club” with “club-members”.
• Thus simplified version of the given question is following
 Question statements Answer statements 1. All clubmembers are students.2. Some clubmembers are married. 3. All married are invited for Dance. a) All students are invited for danceb) All married students are invited for dance c) All club-members are married. d) None of the above conclusions can be drawn

Ok now what?
We’ve to pick up the answer statement one by one and test them.

## a) All students are invited for dance

there are two ways to solve this statement, first the

## longcut method

Who’re the parents of this conclusion statement?
No direct parents. We’ve to apply chainrule.

 Question statements Chain rule All clubmembers(B1) are students(A) We’ll try to link students-clubmembers-married-dance invitation. Some clubmembers(B1) are married.(B2) All married(B2) are invited for Dance.(C)

Let’s start. First two statements

 All clubmembers(B1) are students(A) UP Some clubmembers(B1) are married.(B2) PP

Standard format? Nope.
Conversion needed: yes. But priority order=PP>UN>UP. Means we’ll convert the second statement (particular positive)

 All clubmembers(B1) are students(A) UP Some married (B2) are clubmembers(B1). PP converted to PP.

They’re still not in standard format. So Exchange positions

 Some married (B2) are clubmembers(B1). PP converted to PP. All clubmembers(B1) are students(A) UP

Ok now they’re in standard format. Apply the combo rule. PP+UP=PP (NASA Mood change)
Some married are students. This is our intermediate conclusion. Now pair it up with third question statement from the chain rule

 Some married(B2) are students(A) PP All married(B2) are invited for Dance.(C) UP

Standard format? Nope.
Then convert!

 Some students(A) are married(B2) PP All married(B2) are invited for Dance.(C) UP

Ok now in standard format (A to B then B to C)
Apply combo rule PP+UP=PP (NASA mood change again!)
Conclusion = Some students are invited for dance. (PP)
But the given answer statement says “All students are invited for dance”(UP)=impossible.
Hence first answer choice is eliminated.

## Shortcut

• You see the conclusion statement says “all students are invited for Dance.” (univ.positive statement).
• When do we get “universal positive” statement as conclusion.?
• Only when UP+UP=UP.
• If we apply the chain-rule, we’ll encounter one particular positive (PP). And that’ll ruin the mood (because whenever particular positive statement comes, the conclusion is either

1. PP+UP=Particular positive (NASA mood change) OR
2. UP+PP=No conclusion. (UP politicians hate particular statements).

• Hence we can never get a Universal positive (UP) type of conclusion, in either case! Means this answer choice is invalid by default! No need to manully apply chain rule here. Anyways, Move to the next answer choice

## b) All married students are invited for dance

superficially this statement contains three terms.

1. Married
2. Student
3. Dance

Wait a minute! Our syllogism conclusions contain only two terms (e.g. All dogs are cats.)
So, how can we apply syllogism here?
Well, if you observe carefully, the syllogism rules are still applicable in this conclusion statement containing three terms.
From the “longcut” method in previous option, we’ve found that “Some students are invited for dance. (PP)”

• Question: which students are invited? Well, we eliminated the middle-term (B2) “Married”. Means all married students are invited for dance. (this represents the intersecting area between two Venn Diagram circles).
• Therefore, we can say “All married students are invited for dance.” Hence Answer is (B).

## c) All club-members are married.(UP)

The second question statement says, “Some clubmembers are married.” (PP).
A particular positive statement can be converted into only PP. Hence we cannot say for sure that all club members are married. Hence this answer choice is incorrect.

## DemoQ: Rich n Sick Air travellers (CSAT-2012)

Question Statements

1. None but the rich ran afford air-travel.
2. Some of those who travel by air become sick
3. Some of those who become sick require treatment

Conclusion statements

1. All the rich persons travel by air.
2. Those who travel by air become sick
3. All the rich persons become sick.
4. All those who travel by air are rich

## Solution

• first we will simplify the given statements.
• Recall the “special conversion” rule from earlier article on 2-statement syllogism.
• None but Politicians(A) are honest.(B)=> All honest(B) are politicians(A) (Universal positive)
• Similarly, None but the rich ran afford air-travel=> All air-travellers are rich. (UP).
• That means, Correct answer is (D). Case is over.
• But just for concept clarity, let’s test remaining answer choices as well.
 Simplified question statements All air-travellers are rich. Some air travellers are sick. Some sick are treatment. Simplified Answer statements All rich are air-travellers. (all) air travellers are sick All rich are sick. All air-travellers are are rich.

Now let’s solve

 All rich are air-travellers. The given question statement is “All air-travellers(A) are rich.(B)”(UP). Apply the conversion here, UP=>PP. Hence Some rich(B) are air-travellers(A).Therefore, first answer choice is incorrect. (all) air travellers are sick Question statement #2 says “Some air travellers are sick.” (PP). can’t convert to UP.Hence this option is also incorrect.

## c) All rich are sick.

Q.If this is the conclusion statement, then who are its parents?
Ans. Those question statements which contain the terms “rich”, “sick”, along with a common middle term.
From the given question statements, following two fit the bill

 1. All air-travellers(B) are rich UP 2. Some air travellers(B) are sick PP

## Approach #1 (shortcut)

Please observe: “All rich are sick.”= Universal positive statement.
When do we get UP conclusion? Only when combo rule UP+UP=UP is applied.
Now in above case, one question statement is PP. so it’ll “kill” the mood. UP conclusion is not possible. (no need to convert any statement.)

## Approach #2 (longcut)

 1. All air-travellers(B) are rich.(A) UP 2. Some air travellers(B) are sick.(C) PP

As you can see, there is one middle term (air travellers). But the question statements are not in standard format (A to B then B to C).
It means, we must convert anyone statement. But priority for conversion is PP>UN>UP.
So we will convert second statement.
Some air-travellers are sick (PP)==convert==> Some sick are air-travellers(B)

 1. All air-travellers(B) are rich. UP 2. Some sick are air-travellers(B) PP

But they are still not in standard format (A to B then B to C). well no problem, just exchange position of question statements

 1.Some sick(A) are air-travellers(B) PP 2. All air-travellers(B) are rich.(C) UP

Apply the Combo-rule. PP+UP=PP (NASA Mood change).
Hence Some sick(A) are rich.(C). (PP)
If we convert it then Some rich are sick. (PP convert to PP).
But answer choice says All rich are sick.= this is not possible.
Therefore, third answer choice is also incorrect.

## DemoQ: Drug addict Artists (CSAT-2012)

Question statements

1. All artists are whimsical.
2. Some artists are drug addicts.
3. Frustrated people are prone to become drug addicts.

From the above three statements it may be concluded that:

1. Artists are frustrated
2. Some drug addicts are whimsical
3. All frustrated people are drug addicts.
4. Whimsical people are generally frustrated

Statement 3 says “Frustrated people are prone to become drug addicts.” For our purpose this is a “Particular positive (PP)” statement. Let’s simplify it to “Some frustrated people are drug addicts” Now start with answer (A)

## a) (all) Artists are frustrated (UP)

if this is the answer, then what could be the question statements?
The question statements could be those statements where the words Artist and frustrated come along with a common middle-term (B)
Consider these question statements:

 2. Some artists are drug addicts.(B) PP 3. Some Frustrated people are drug addicts.(B) PP

Although this in not in “standard format”, but even when we convert one of them (PP->PP), we’ll be left with PP+PP=no conclusion.
Hence move to next option.

## b) Some drug addicts are whimsical

• if this is the answer, then what could be the question statements?
• The question statements could be those statements where the words drug addict and whimsical come along with a common middle-term (B)
• Consider these question statements:
 1. All artists (B) are whimsical. UP 2. Some artists (B) are drug addicts. PP
• Three terms = yes.
• Standard format (A to B then B to C)=No.
• So maybe to convert anyone know the statement. according to the priority order PP>UN>UP, we must convert second statement.
 1. All artists (B) are whimsical. UP 2. Some drug addicts are artists (B). PP->PP converted.

Now interchange position of question statement 1 and 2.

 Some drug addicts(A) are artists (B). PP->PP converted. All artists (B) are whimsical.(C) UP
• Okay now what? Apply the combo rules
• PP+UP=PP. (NASA mood change).
• Thus final answer is “some drug addicts are whimsical.” (option B)

For the archive of all [Aptitude] articles, visit Mrunal.org/aptitude.

## Mrunal recommends

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

## 233 Comments on “[Reasoning] Three-Statement Syllogism: technique, method, shortcuts for IBPS, SSC, CSAT, CAT, CMAT”

1. Statements: (rrb po 2012)
All stars are bottles
some bottles are papers
No paper is calander

Conclusion 1 :
1 All stares being papers is a possibility
2 No calander is a paper

Conclusion 2 :
1 All calander being stars is a possibility
2 Atleast some bottles are stars

Sir plz explain how to deal with term ” being______ a possibility “

1. in both the conclusion
conclusion 2 follows

1. manish jab tujhe kuchh nhi ata to dusron ko kyun bevkuf bnarha h is qsn m dono m dono option shi h .

2. thank u very muchhh…….itss very easy trick than all other tricks i had studied

3. Guys i m appearing for the IBPS PO for the first time…pls suggest me a book whrein the syllogisms are explained using venn diagrams…i am not getting this UP UN and AEIOU method atall….pls pls pls pls help me

4. this site is very useful.
thankuu so much sir
plz also tell us how to deal with being a possibility conclusions by this method

5. Statements: Only pink is red
Some pink are blue.
No blue is white.
Conclusions: I. All pink, if they are blue are also white.
II. At least some pink being white is a possibility.

I am finding it difficult to decide about conclusion-1 in the above question.
Plz reply as soon as possible.

Rajat

1. Conclusion II follows.
I cant follow because no blue is white then how pink if blue can be white.

2. i think no conclusion is a the right ans

6. 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

1. only conclusion 3 and 4 follows

7. anyone knows the 100:50 method for solving syllogsms

1. Hey! Could you please tell me the 100:50 method if you have figured it out. I really need it. Thank you.

8. All fans are tube lights.
No pen is a bulb.
Some bulbs are fans.

Conclusion:
I. Some fans are not pens
II. All bulbs being tube lights is a possibility

Choice:
1) only I
2) only II
3) either I or II
4) neither I or II
5) both I and II

1. both 1 and 2

9. Statements:
Some cups are utensils.
No utensil is a bucket.
All buckets are plates.
Conclusions:
I. Some cups are buckets.
II. Some utensils are plates.
III. No utensil is a plate.
IV. Some cups are plates.
1) Only I follows
2) Only III follows
3) Either II or III follows
4) Either III or IV follows
5) None of these
Ans:-3
As per my calculation ans should be 4.

1. only conclusion 3 follows

1. Hi ..how did you solve this …
Statements:
Some cups are utensils.
No utensil is a bucket.
All buckets are plates.
Conclusions:
I. Some cups are buckets.
II. Some utensils are plates.
III. No utensil is a plate.
IV. Some cups are plates.
1) Only I follows
2) Only III follows
3) Either II or III follows
4) Either III or IV follows
5) None of these

10. Thanks Mrunal for clearing doubts on special cases like none, any etc

11. sir plz tell me how to solve the problem of syllogism when answer choice asking about the possibilites of the conclusion statement

12. sir iam very confused in possibility cases in 3statements so can u explain clearly in diz example Statements.
1.all apartments are hut
2.No hut is building
3.all buildings at cottage

Conclusions
1.no cottage is apartment
2.some cottages are apartment
3.No apartment is a cottage
4.Some buildings being apartment is a possibility
5.Some cottages being apartment is a possibility
6. No cottage is a hut.

in 4th & 5th stmt im confusing so plz tell me clearly

1. None of the conclusion follows .is that the answer. i can be wrong so please dont mind.

13. Hi All,

In the above question of drug addict, why cant we take the below statement as a universal statement.
How are we applying this special conversion in these statements.

Frustrated people are prone to become drug addicts.

Can anyone explain this scenario.

Thank you !!

14. sir,
up un technique is really helpful and accurate. Although practice is key 2 success bt some useful techniques like this are beneficial and time saving..As promised in the beginning that once practicwd it will be like a walk in the park and you deliveried it.

If i am not asking for much than can u please post an artcle on data interpritation DI .it is an very humble request please look into it.
thank you

15. Question:
Parent statements;

a) All chalks are cheese
b) No cheese is a ship
c) Some herds are ships

Conclusions:

1. Some herds are not chalks
2. Some herds are not cheese.
3. Some cheese are not herds.
4. No chalk is a ship.

a) only 2 and 4 follow
b) 1, 2 and 4 follow

My doubt:
If i take conclusion 4 as an intermediate conclusion and couple it with parent statement c, i get the result that conclusion 1 follows.
But if i take conclusion 2 as an intermediate conclusion and couple it with parent statement a, i get the result that conclusion 1 doesn’t follow.

Is there any rule regarding the choice of intermediate conclusions: kindly solve my conundrum.

16. Mrunal Sir, please explain the below in detail conclusion having 3 terms…..

b) All married students are invited for dance

superficially this statement contains three terms.

Married
Student
Dance
Wait a minute! Our syllogism conclusions contain only two terms (e.g. All dogs are cats.)
So, how can we apply syllogism here?
Well, if you observe carefully, the syllogism rules are still applicable in this conclusion statement containing three terms.
From the “longcut” method in previous option, we’ve found that “Some students are invited for dance. (PP)”

Question: which students are invited? Well, we eliminated the middle-term (B2) “Married”. Means all married students are invited for dance. (this represents the intersecting area between two Venn Diagram circles).
Therefore, we can say “All married students are invited for dance.” Hence Answer is (B).

17. Statements:
1.No house is an apartment
2.some bungalows are apartment
Conclusion:
1.No house is bungalows
2.All bungalows are houses

pls., any one conclude the answer with proper explanation..

the answer is Either 1 or 2 in the booklet… is dis correct..

18. pls solve tis questions iam bit confused.

(A) if only conclusion I is true.
(B) if only conclusion II is true.
(C) if either conclusion I or conclusion II is true.
(D) if neither conclusion I nor conclusion II is true.
(E) if both conclusions I and II are true.

Statements :
All switches are plugs.
Some plugs are bulbs.
All bulbs are sockets.
Conclusions :
I. Some sockets are plugs.
II. Some plugs are switches.

A

B

C

D

E

Statements :
All curtains are rods.
Some rods are sheets.
Some sheets are pillows.
Conclusions :
I. Some pillows are rods.
II. Some rods are curtains.

Statements :
All stars are suns.
Some suns are planets.
All planets are satellites.
Conclusions :
I. Some satellites are stars.
II. No star is a satellite.

B
C

19. sbi po 2011 ques-
statements-
1. all rings are circles
2. all squares are rings
3. no ellipse is a circle
conclusion-
1.some rings being ellipses is a possibility
2. at lest some circles are squares.

i m unable to solve the question, pls help sir

1. In the above question, the answer is ONLY 2 is true. becoz ellipse is having no link with with either of first statements..

2. The answer is only II. B

20. Can anyone plz explain?
Statements 1. All actors are males
2. Some artists are males
3. All singers are artists
Conclusions I. some artists are actors
II. some singers are males
III. some males are actors
IV. No singers are males
a) only either II or IV & III follows
b) only either II or IV & I follows
c) only either I or II & IV follows
d) none follow
e) none of these

1. a

21. sir my ques is
some clocks are mobiles.no torch is a clock.all lamps are torches.
conclusion1:some lamps being clocks is a possibility.
con2:No mobile is a torch.
1:Either 1 or 2 follows
2:only 2 follows
3:both 1 and 2 follows
4:only 1 follows
5:neither 1 or 2 follows
plz provide ans with sol and specify about being statement.

1. 5:neither 1 or 2 follows
for conclusion 1:
all lamps are torches.—–A
no torch is a clock———–E
A+E=E;
Conclsion comes- No lamps are clock—-E, hence conclusion 1 not possible.
For conclusion 2:
no torch is a clock—-E
some clocks are mobiles——–I
E+I=O*
i.e. some mobile r not torch.===this doesnt mean “No mobile is a torch.”

hence neither follows

1. Rakeysh is there any order to solve Syllogism question i mean 1 and 2 or 2 and 3

plz explain this question with this formula method you are using .

Some keys are staplers. Some staplers are stickers. All the stickers are pens.

Some pens are staplers.
Some stickers are keys.
No sticker is key.
Some staplers are keys.

A. Only (1) and (2)
B. Only (2) and (4)
C. Only (2) and (3)
D. Only (1) and (4) and either (2) or (3)

22. Thank u mrunal…….

23. sir i want more examples for three statement syllogism…can you please guide me sir?

24. sir i want to know about when the possibility statement is correct and when atleast some is correct please explain it sir…

25. Some clips are copies. Some copies are magazines. No magazines is a dictionary.
Conclusions:
1. No copies are dictionary.
2. Some copies are dictionary.
3. Some copies are not dictionary.
4. No clips are magazines.

only 3 follows
only either 1 or 2&3 follows
only 1 follows
only either 1 or 2 follows

1. only either 1 or 2&3 follows

26. sir , i am using ven diagram to find relation , i am correlate relation much faster , is there any disadvantage to that ????

27. Statements : All married are men, Some men are educated
conslusions: some married are educated, some educated are married

If i arrange it in the form A to B and B to C it becomes

Some married are men
some men are educated
so two particulars equal to no conclusion

but in RS Agarwal reasoning book it is given both conclusion follows

how is that possible? guys please someone help me

28. question typo error.

All married are men, Some men are educated
conslusions: some married are educated, some educated are married

statements:
1)all star are bottles
2)some bottles are papers
3)no paper is a calendar

conclusions
1)atleast some calendars are bottles
2)no calendar is a star

options
1)only conclucion 1 follow
2)only conclucion 2 follow
3)either 1 or 2 follow
4)neither 1 or 2 follow
5)both 1 and 2 follow

30. Anyone plz plz help me .. i have tried so hard to learn syllogism but still not able to solve them clearly . i am solving using formula to solve them for example question

All the locks are keys. All the keys are bats. Some watches are bats.

Conclusions:

Some bats are locks.
Some watches are keys.
All the keys are locks.

A. Only (1) and (2)
B. Only (1)
C. Only (2)
D. Only (1) and (3)

My steps to solve this question is

1 ) combine first and second statement that is
All the locks are keys.
All the keys are bats.

then conclusion is : All the locks are bats using All +All= All formula

Now Come to the second and third statement

All the keys are bats.
Some watches are bats.

Now i convert third statement to something like : Some bats are watches to make 2 and 3 statement in the form of A-B /B-C

then according to rule All +Some = No Conclusion.

and at last i followed Conversions like (all’ can be converted to ‘some’
‘some can be converted to ‘some’ .
‘no’ can be converted to ‘no’. ) to see if any conclusion matches the conversion .

according to me answer should be * None Follows .. which is not in the option :(

Guys plz help me to solve this and correct me which step i am doing wrong …