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.
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:
- Some actors are dancers.
- No singer is actor.
Answer: Option
Explanation:
Discussion:
78 comments Page 3 of 8.
Shreyas Alagundi said:
10 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.
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.
(3)
Rahul kumar said:
1 decade ago
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.
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.
(1)
Pavi said:
1 decade ago
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).
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).
RICHA said:
1 decade ago
What with negative statements?
Kiran said:
1 decade ago
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.
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.
Seema said:
1 decade ago
You have study logic first. Can you solve mathematical problems without knowing formulas. There's no short cut.
Prakash singh said:
1 decade ago
Very easy some actors are singers and all singers are dancer.
Kalpa said:
1 decade ago
Reasoning is the best way to solve than any tricks. Read the question twice to get the answer.
Manasa said:
1 decade ago
How to solve syllogism questions?
Trishul said:
1 decade ago
@Rajani, "All actors are dancers' can be converted into 'some actors are dancers' but not vice versa.
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