Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known f act s, decide which of the conclusions logically follow(s) from the statements. Statements: Some carpenters are singers. All singers are doctors. Conclusions: I. No doctor is a carpenter. II. Some doctors are singers. III. Some carpenters are doctors.
Only conclusions II and III follow
Understanding Syllogism Statements and Conclusions
This question tests your ability to analyze given statements and determine which conclusions logically follow from them. We are given two statements and three conclusions. We must assume the statements are true, even if they contradict general knowledge.
Analyzing the Statements
We have the following statements:
- Statement 1: Some carpenters are singers.
- Statement 2: All singers are doctors.
To solve this, we can visualize the relationships using Venn diagrams or apply rules of logic. Let's represent Carpenters as 'C', Singers as 'S', and Doctors as 'D'.
- Statement 1 means there is an overlap between the set of Carpenters and the set of Singers. Some elements are common to both C and S.
- Statement 2 means the entire set of Singers is contained within the set of Doctors. Every element in S is also in D.
Combining the Statements
If some carpenters are singers (Statement 1), and all singers are doctors (Statement 2), then the carpenters who are also singers must necessarily be doctors as well. This creates a link between Carpenters and Doctors through the medium of Singers.
Evaluating the Conclusions
Let's evaluate each conclusion based on the combined information from the statements.
Conclusion I: No doctor is a carpenter.
From our combined analysis, we know that some carpenters are singers, and all singers are doctors. This means the group of carpenters who are also singers are automatically part of the group of doctors. Therefore, some doctors *are* carpenters. This conclusion contradicts the information derived from the statements. So, Conclusion I does not logically follow.
Conclusion II: Some doctors are singers.
Statement 2 explicitly says, "All singers are doctors." If every single singer is a doctor, then it must be true that there are some doctors who are singers (the group of singers itself is a part of the group of doctors). This is a direct and valid inference from an 'All' statement. So, Conclusion II logically follows.
Conclusion III: Some carpenters are doctors.
Statement 1 tells us "Some carpenters are singers". Statement 2 tells us "All singers are doctors". Let's consider the group of people who are both carpenters and singers (according to Statement 1). Since, according to Statement 2, everyone who is a singer is also a doctor, then this group of carpenter-singers must also be carpenter-doctors. Thus, there are some individuals who are both carpenters and doctors. So, Conclusion III logically follows.
Summary of Findings
Based on our analysis:
- Conclusion I: Does not follow.
- Conclusion II: Follows.
- Conclusion III: Follows.
Therefore, only conclusions II and III logically follow from the given statements.
Revision Table: Syllogism Rules
| Statement Type | Example | Valid Immediate Inferences | |||
|---|---|---|---|---|---|
| All A are B | All dogs are mammals. | Some A are B, Some B are A (Conversion by limitation), No A are Non-B. | |||
| No A are B | No cat is a dog. | No B are A (Simple Conversion), Some A are not B, Some B are not A. | |||
| Some A are B | Some students are clever. | Some B are A (Simple Conversion). | Some A are not B | Some students are not lazy. | No immediate valid conversion or other simple inferences. |
In this problem, "All singers are doctors" is an 'All S are D' statement. A valid inference from this is "Some D are S", which is Conclusion II.
Additional Information: Types of Syllogistic Statements
Syllogism problems use standard categorical statements. There are four types:
- Universal Affirmative (A): All S are P (e.g., All cats are animals). The entire subject group is included in the predicate group.
- Universal Negative (E): No S are P (e.g., No dogs are cats). The entire subject group is excluded from the predicate group.
- Particular Affirmative (I): Some S are P (e.g., Some birds are black). At least one member of the subject group is included in the predicate group.
- Particular Negative (O): Some S are not P (e.g., Some students are not tall). At least one member of the subject group is excluded from the predicate group.
Understanding these types helps in applying the correct logical rules or drawing accurate Venn diagrams.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
Read the given statements and conclusions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some pillows are doors.
Some doors are beds.
Conclusions:
I. Some doors are pillows.
II. All beds are doors.
Important Questions from Syllogism
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
