Verbal Reasoning - Syllogism - Discussion

In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Give answer:

  • (A) If only (1) conclusion follows
  • (B) If only (2) conclusion follows
  • (C) If either (1) or (2) follows
  • (D) If neither (1) nor (2) follows and
  • (E) If both (1) and (2) follow.

1. 

Statements: Some actors are singers. All the singers are dancers.

Conclusions:

  1. Some actors are dancers.
  2. No singer is actor.

[A]. Only (1) conclusion follows
[B]. Only (2) conclusion follows
[C]. Either (1) or (2) follows
[D]. Neither (1) nor (2) follows
[E]. Both (1) and (2) follow

Answer: Option A

Explanation:


Riyaz said: (Nov 3, 2010)  
Hello please we Need some fast sloving method needed. Who's know Tell me Here Friends.

Priyanka said: (Nov 22, 2010)  
Here it is given that some actors are singers and every singer is a dancer so actors are all dancers.

Its just like a=b,b=c then a=c.

Chiru said: (Dec 9, 2010)  
Tell me the solving of syllogism problems in another way,rather than Venn diagram approach.

Nihar said: (Dec 31, 2010)  
I would like to say that , if a=b, b=c, then a=c , but is it true for c=a .

Rashmi said: (Jan 12, 2011)  
Why all the actors are concluded as dancers? in one of venn diagram.

Seema said: (Feb 24, 2011)  
@Rashmi

All actors are not concluded in any diagram, it shows some actors are dancers.

Samarjit said: (Mar 7, 2011)  
Does the logical deduction step of conversion and implification is also applied here along with the venn diagram to get the conclusion?

Tapan said: (Mar 12, 2011)  
Hello friends I have a short technique,

In here no need to draw diagram. If two statement is given then 1st look the mediator if it contain ALL, NO then close ur eyes and sure that it is distributiv if the mediator have no ALL, No then the conclusion has a -ve term.

Let eg
some actor are dancer
all dancer are singer
ANS; some actor are singer/some singer are actor
some actor are dancer
some dancer are singer
ANS; some singer are not dancer

Silvia said: (Mar 28, 2011)  
We are very Confuse in this Method can you tell me in easy way.

J.Rahim said: (Mar 30, 2011)  
I am very confused in this method. Because how use big diagram and small diagram. You should tell the method.

B.Veeranna said: (Apr 11, 2011)  
Tell me which diagram suitable for answering the question.

Ashish Mishra said: (Apr 30, 2011)  
There is farmula if some + all = some

statement is 1- Some actors are singers.
2- All the singers are dancers.

Than as per rule some will come and singers is comman for both sentences hence that would be cancelled and conlusion will come as ---- some actors are dancers.

Deepthi said: (May 23, 2011)  
let ALL=A,SOME=E
formula
A+A=A
A+E=NO CONCLUSION
E+E=NO CONCLUSION
E+A=E
A-->E (A conversion is E)
E-->E

eg:1.Some actors are singers.
2.All the singers are dancers

as per the rule E+A=E
first see common in both sentences is singers that singers is cancelled then conclusion will comes as some actors are dancers or some dancers are actor or some singers are actors or
some dancers are the singers


eg:1.All books are trees.
2.All trees are lions.
as per the rule A+A=A ,A-->E
then conlusion is All books are lions or some lions are books or some trees are books or some lions are trees

Amrutha said: (May 25, 2011)  
HAI DEEPTHI.............THIS IS AMRUTHA
CAN U EXPLAIN BELLOW WHICH IS WRITEN BY U

let ALL=A,SOME=E
formula
A+A=A
A+E=NO CONCLUSION
E+E=NO CONCLUSION
E+A=E
A-->E (A conversion is E)
E-->E

Harmandeep Singh said: (May 27, 2011)  
HAI DEEPTHI.......This is Harmandeep Singh
would u please explain me these term
A-->E (A conversion is E)
E-->E
and as well as in ur 1st example those lines meaning i.e."then conclusion will comes as some actors are dancers or some dancers are actor or some singers are actors or
some dancers are the singers"

eg:1.Some actors are singers.
2.All the singers are dancers

as per the rule E+A=E
first see common in both sentences is singers that singers is cancelled then conclusion will comes as some actors are dancers or some dancers are actor or some singers are actors or
some dancers are the singers


eg:1.All books are trees.
2.All trees are lions.
as per the rule A+A=A ,A-->E
then conlusion is All books are lions or some lions are books or some trees are books or some lions are trees

Dharma29999 said: (Jun 19, 2011)  
HI, everybody
some tips to crack a syllogisms problems.

We follow the certain rules of syllogisms,
one can solve the venn diagrams and other solved by others method.
but shortcut is very simple.

Example:
some dogs are cats.
all cats are horses.
we follow the rules of syllogisms
some+all= some
and we also cancle the cats, because it is common for both the statement.
condition: 1. all dogs are horses.
2. somes dogs are horses. (answer)
3. some horses are not dogs.
we can always see the condition then solve syllogisms problem
firstly we cancle the cats matching with two statement.
and according to rules we can check (some+all= some) for two sentence syllogisms.
and after we analise some dogs are horses to match the condition.
it the answer.

Monal said: (Jul 19, 2011)  
@Deepti

First of all I would like 2 thank you both for such wonderful trick.

But what should we do if the ststement contains NO.

Ex: No cats are dogs etc etc.

Mani Latha said: (Jul 23, 2011)  
By seeing Venn diagrams you can't able to get point. If possible tell us in different manner.

Akhil said: (Aug 12, 2011)  
Very easy. If one is particular definitely conclusion should be particular (particular means come) without middle term.

Dheeraj Sri said: (Aug 25, 2011)  
Can any1 tell in what condition the option ' C ' wl b the answr.? I dint find any qustn here whose answr is C ?

Divya said: (Sep 14, 2011)  
Hi can any one please explain I am confusing a lot in this method.

Rami Reddy said: (Oct 3, 2011)  
OPTION C is correct when (if stmt1 true then stmt2 false) or (if stmt2 true then stmt1 false)

Ravinder Kumar said: (Jan 4, 2012)  
A - s, SS - D conclusion A - D follows from Raval's notation second conclusion SS /AA is straightaway ruled out by Raval's notation

Dinesh said: (Jan 12, 2012)  
In above statement you shold know that is the both statement is affirmative than the conclusion can not be negative statement.

Yamuna said: (Apr 25, 2012)  
Hai. friends
Actually syllogism has ,the statements could therefore be classified into the following two types
a) universal propositions like"all" or " none"
ex: All lecturers are research scholars.
No student refers to research study material.
b)particular propositions like " some" or "some...not"
eg: Some vehicles are cost prohibited.
Some roads are not good.
And the syllogism statement has two types
Interference and Conversion
In interference.. there is no change in subject and predicate.
for ex:
in contraverse, conversion has interchanged their subject and predicate.
there is some simple formula that is easy to memories
Denote "All as A"
"NO as E"
"Some as I"
"Some ..not as O"
formula,
In interference
A=A
E=I
In Conversion,
A=A
E=E
I=I
Eg:
1.All Students are music lovers-A
NO music lover is cruel- E
(Here "All denotes A
so A=I and E=O)

Answer: (Interference)
Some students are music lovers
Some music lover are not cruel
(here, no change in subject(students) and predicate(music lovers)

(In Conversion)
Some music lover are students
No cruel is music lover
(here there is change in subject and predicate)

Rajni said: (Jun 2, 2012)  
@Yamuna. I am unable to understand about interference and conversion, can you explain it in a different way ?

Suganya said: (Jul 25, 2012)  
In second diagram its shown all actors are dancer.

In first some actor are dancer.

If both possibility are true then only conclusion occurs.

So neither 1 nor 2 should be the answer.

Why conclusion I is selected?

Kumar Sourabh said: (Nov 25, 2012)  
I want to know these 2 crucial facts about syllogism: First, we all know that 'No and Some'/'Some and some not' form an either case or a complimentary pair, but does 'All and No' form a complimentary pair...Second, what is the difference in approach of these two statements:

1.All stones are glass.
2.All stones being glass is a possibility.

Lovely said: (Feb 18, 2013)  
When to converse a sentence?

Anand said: (Jul 2, 2013)  
Here first diagram is OK but (or) diagram implies that all the singers and actors are dancers if any body please explain it in detailed manner.

Achal said: (Jul 7, 2013)  
Conclusion: all actor which are not dancer can never be singer. Is this conclusion true or not?

Manoj said: (Dec 26, 2013)  
A - S, SS - D conclusion A - D follows from Raval's notation second conclusion SS /AA is straightaway ruled out by Raval's notation. Raval's notation is new simplest and quickest way to solve syllogism problems at a glance. Search 'raval notations at philpapers' in google and find complete new and simple approach published at University of London.

Faliot Chibwe said: (Jan 17, 2014)  
Can you elucidate what it means & to use Raval's notation.

Srujana said: (Mar 21, 2014)  
Hi friends!

Can anyone post all the rules regarding syllogisms with an example, in a step by step procedure. These are tough to me.

Rupesh said: (Apr 10, 2014)  
Hello friends!

Anyone can tell me east and suitable method to solve syllogism so I can calculate very fast?

Vikas A said: (Aug 3, 2014)  
All I can say is done use venn diagram method because its just results in frustration am I right? so here we go, use UP/UN method to solve syllogism. Its difficult to understand but if you get the perfect idea you can solve syllogism easily.. Shocking? but trust me guys it needs hours of practice to master in that but when you got that trick you can solve syllogism in your mind no need of pen pencil paper etc etc. So guys what for you still waiting just google it (UP-UN method) thats it my friends.

Shabeen said: (Sep 10, 2014)  
First know All=A, NO=E, SOME=I, O=SOME NOT, O* = O revers.

Let A+A=A.
A+E=E.
E+A=O*.
E+I=O*.
I+A=I.
I+E=O.
A+I=NC(no conclusion).
A+O=NC.
I+I=NC.

FOLLOW THIS METHOD A LITTLE BIT EASY TO SOLVE.

Priya said: (Sep 23, 2014)  
I can't understand second diagram, please explain it.

Yelena said: (Oct 5, 2014)  
I am not at all understanding any of the above methods please tell me an easy method.

Faraz said: (Nov 22, 2014)  
Hello All,

This is only for those who are very poor to understand syllogism. I assure you can understand very well through my given examples.

Here already discussed that.

*. ALL+ALL = ALL.

Means Suppose All Pens are chair & ALL chairs are tables.

It means that both the statements have all in First.

So, this can be written as All pens are tables.

Hope you understand well.

Suresh said: (Dec 26, 2014)  
'Some actors are singers. All the singers are dancers'.

Then why in the 2nd venn diagram all actors are dancers. I understood the first venn diagram but not the second.

Please help.

Ravinder said: (Mar 31, 2015)  
Venn diagram (Correctly Euler circles) shows all possibilities which do not violates any given premises. All actors are dancers do not violate any given premise. So it is shown in the diagrams.

Amit Kumar said: (May 9, 2015)  
I want to know about negative sentence.

Priyanka said: (Jun 2, 2015)  
All cards being papers is a possibility. What is its meaning?

Sindhu said: (Jun 3, 2015)  
For question 2 in examples, I feel option (1) follows.

Some asses are not dogs is true right? since some asses are bulls (which implies they're not dogs). Please reply why not?

Rajani A S said: (Jun 19, 2015)  
Please help me anyone to understand syllogism in simple way.

Akilan said: (Jul 13, 2015)  
Why not all actors are dancers? 2nd diagram very much confused.

Gaurav said: (Jul 18, 2015)  
Is there any other easier trick?

Trishul said: (Jul 22, 2015)  
@Rajani, "All actors are dancers' can be converted into 'some actors are dancers' but not vice versa.

Manasa said: (Sep 5, 2015)  
How to solve syllogism questions?

Kalpa said: (Nov 21, 2015)  
Reasoning is the best way to solve than any tricks. Read the question twice to get the answer.

Prakash Singh said: (Dec 3, 2015)  
Very easy some actors are singers and all singers are dancer.

Seema said: (Mar 1, 2016)  
You have study logic first. Can you solve mathematical problems without knowing formulas. There's no short cut.

Kiran said: (Jun 13, 2016)  
There should be common term present between two conclusions in case if conclusion contains NO.

Then the only answer will be either or option.

Eg- all men's are a duck.

NO men are duck.

If I'm wrong correct me.

Richa said: (Aug 3, 2016)  
What with negative statements?

Pavi said: (Aug 18, 2016)  
All squares are circles.
All circles are units.
No circle is a meter.

Conclusions:.

I. Some units which are not circles can be meters.

II. Some squares being meters is a possibility.

(Anyone please explain how to solve this using formula table).

Rahul Kumar said: (Sep 10, 2016)  
Statements:

All squares are circles.
All circles are units.
No circle is a meter.

Conclusions:

I. Some units which are not circles can be meters.

II. Some squares being meters is a possibility.

Anyone please explain how to solve this using formula table.

Shreyas Alagundi said: (Sep 22, 2016)  
METHOD TO SOVE THESE TYPE OF PROBLEMS

In Transformed RAVAL\'S NOTATION, each premise and the conclusion is written in abbreviated form, and then the conclusion is reached simply by connecting abbreviated premises.

NOTATION: Statements (both premises and conclusions) are represented as follows:

Statement Notation

a) All S are P SS-P
b) Some S are P S-P
c) Some S are not P S / PP
d) No S is P SS / PP
(- implies are and / implies are not)

All is represented by double letters; Some is represented by a single letter. Some S are not P is represented as S / PP. No S is P implies No P is S so its notation contains double letters on both sides.

RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle\'s rule: the middle term must be distributed at least once).

(2)If both statements linked are having " signs, resulting conclusion carries " sign (Aristotle\'s rule: two affirmatives imply an affirmative).

(3) Whenever statements having " and / signs are linked, resulting conclusion carries / sign. (Aristotle\'s rule: if one premise is negative, then the conclusion must be negative).

(4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle\'s rule: Two negative premises imply no valid conclusion).

Following illustrations will make the above rules very clear illustration:

Statements ------ Notation
a) All S are P ------ a) SS " P
b) All P are Q ------ b) PP- Q

Valid Conclusions:
1. All S are Q ------>1.SS -Q
2. Some S are Q ------>2.S "Q
3. Some Q are S ------>3.Q "S
4. Some P are S ------>4.P "S
5. Some Q are P ------>5.Q- P
6. Some S are P ------>6.S- P
7. Some P are Q ------>7.P-Q

Wrong Conclusions:
1.All Q are S ------>1.QQ-S
2. All P are S ------>2.PP-S
3. All Q are P ------>3.QQ -P
4 Some S are not Q. ------> 4. S / QQ
5. Some Q are not S ------>5.Q / SS
6. Some P are not S ------>6.P / SS

Explanation: From

a) SS " P
b) PP "Q

Valid Conclusions:
SS " Q follows, because here common linking term (P) multiplies.
S- Q follows because Some is part of All(S is included in SS but not vice versa) and common linking term (P) multiplies.
Q- S follows because here common linking term (P) divides.
P- S follows from the main statement SS " P (by reverse reading).
Q " P follows from the main statement PP " Q (by reverse reading, one can isolate P from PP).
S " P follows from the main statement SS " P.
P " Q follows from the main statement PP " Q.

Wrong Conclusions:
1. QQ " S does not follow because we don\'t have any QQ in statement notation.
2. PP " S does not follow because there is no common linking term between PP and S.
3. QQ " P does not follow because we don\'t have any QQ in statement notation.
4. S / QQ is ruled out because we don\'t have any / sign in statement notation.
5. Q / SS is ruled out because we don\'t have any / sign in statement notation.
6. P / SS is ruled out because we don\'t have any / sign in statement notation.

Vidhya said: (Oct 17, 2016)  
Please explain the UP-UN METHOD in detail.

Shikha said: (Nov 24, 2016)  
@Deepthi.

Your concept is wrong. No need to find out conclusion, they already given in the question. In this chapter, the statement is given and the conclusion is also given we prove that conclusion is wrong or not. If the conclusion is wrong then you are right, or conclusion is right then you are wrong.

Notes: [ (All=some not, not) (some=no) (no=all, some) ]. Always remember this, it used in conclusion to proving right ya wrong. This is your opposite words.

For example statement 1: All hands are arms, some hands are skins.

Conclusion 1: some skins are arms.

2: All skins are arms.

Answer: draw a diagram for the help of statement. And prove the statement for the help of conclusion.

1: Some skins are arms (some change into no).

2: all skins are arms (all change into not / some not).

So, conclusion 1st is the correct answer.

Thank you, everybody.

Shikha.

Dipesh said: (Jan 9, 2017)  
Please, anybody can explain this clearly? I am confused.

Roshan said: (Jan 14, 2017)  
In second diagram. All actors are dancer comes out. And in first some actors are dancers. If the statement is not satisfying both the diagrams, then how we can say one is correct?

Please explain.

Ravi Kumar said: (Jul 5, 2017)  
2nd Venn diagram shows that all actors are dancers. Then, why option A is correct?

Kamal said: (Oct 23, 2017)  
Hi,

Can anyone explain it in short? Because I couldn't get the "some are not " model.

Statements:
All squares are circles.
All circles are units.
No circle is a meter.

Conclusions:

I. Some units which are not circles can be meters.
II. Some squares being meters is a possibility.

Anyone, please explain how to solve this using formula table.

Suman said: (Dec 6, 2017)  
Let A- all (eg- all trees are dog.)
B- all not (eg- all trees are not dog.)
Z- some (eg- some trees are dog.)
Y- some not(eg- some trees are not dog.)

A can be converted to Z(eg- All trees are dog. conversion- some trees are dogs. (or) some dogs are tree)
B can be converted to B or Y((eg- All trees are not dog. conversion- all dogs are not tree. (or) All trees are not dog))
Z can be converted to z(eg- some trees are dogs.conversion- some dogs are trees.)
Y has no conclusion.

Combination :
A+A = Z.
A +B = Z.
A+Z = no conclusion.
A+Y= no conclusion.

B+A = Y.
B +B = no conclusion.
B+Z = Y.
B+Y= no conclusion.

B+A = Z.
B +B = Y.
B+Z = no conclusion.
B+Y= no conclusion.

Y + (A, B, Z)= no conclusion.

Huraira said: (Jan 15, 2018)  
@SUMAN

you repeated
B+A = Y.
B +B = no conclusion.
B+Z = Y.
B+Y= no conclusion.

B+A = Z.
B +B = Y.
B+Z = no conclusion.
B+Y= no conclusion.

Which combination is now correct?

Tusar said: (Aug 12, 2018)  
@All.

Always solve from the conclusion. If both the statement have a common and all is attached with that common word. Then conclusion true. Ex here common is a singer. And singer Se pehele all he. So directly some actors are dancers. Next, for conclusion 2 we can't draw -ve conclusion from positive statements. So false.

Waheed said: (Apr 23, 2019)  
How first conclusion follows? I think either is the right answer.

Ladshika Mohan said: (Jan 28, 2021)  
Here, 2nd diagram is wrong one and instead of that, the three circles become intersect and the inside circle mentioned singers next circle mentioned dancers and outside circle mentioned actors, this should be right.

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