Verbal Reasoning - Syllogism - Discussion

How first conclusion follows? I think either is the right answer.

Option A is correct. I agree with the given answer.

Agree, Option A is correct.

Option A is correct. Only conclusion 1 follows.

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.

Agree, Only 1 conclusion follows.

@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.

Yes, @Waheed.

It's correct because there is no cross between actor, dancer or singer.

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.

@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?