# Verbal Reasoning - Syllogism - Discussion

Discussion Forum : Syllogism - Syllogism 1 (Q.No. 1)
Directions to Solve

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.

• (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.

Only (1) conclusion follows
Only (2) conclusion follows
Either (1) or (2) follows
Neither (1) nor (2) follows
Both (1) and (2) follow
Explanation:
Discussion:
73 comments Page 1 of 8.

Shreyas Alagundi said:   8 years ago
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.
(2)

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.
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)

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)

Shikha said:   8 years ago
@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.

Harmandeep Singh said:   1 decade ago
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

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.

Suman said:   7 years ago
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.
(2)

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

Vikas A said:   1 decade ago
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.

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
(1)

Faraz said:   10 years ago
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.

*. 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.