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.
Only conclusion I follows
Understanding Logical Reasoning Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow based on these statements, even if they contradict general knowledge. This is a common type of logical reasoning problem involving syllogisms.
Analyzing the Given Statements
We have three statements:
- Statement 1: No city is a district.
- Statement 2: Some districts are zones.
- Statement 3: Some zones are states.
Let's represent these relationships:
- Statement 1 establishes a complete separation between 'city' and 'district'. There is no overlap.
- Statement 2 indicates a partial overlap between 'districts' and 'zones'. At least one district is a zone.
- Statement 3 indicates a partial overlap between 'zones' and 'states'. At least one zone is a state.
Analyzing the Given Conclusions
We need to evaluate three conclusions:
- Conclusion I: Some zones are districts.
- Conclusion II: Some districts are cities.
- Conclusion III: No state is a zone.
Evaluating Each Conclusion
Let's examine each conclusion in light of the given statements:
Evaluating Conclusion I: Some zones are districts.
Statement 2 says, "Some districts are zones." This means that the set of districts and the set of zones have at least one element in common. If we say "Some districts are zones," it directly implies that there are some entities that are both districts and zones. The statement "Some zones are districts" expresses the same relationship from the perspective of zones. This is a direct conversion of the original statement type (I type). The converse of an I-type proposition is always valid.
Therefore, Conclusion I logically follows from Statement 2.
Evaluating Conclusion II: Some districts are cities.
Statement 1 says, "No city is a district." This is a universal negative statement. It means that the sets of 'city' and 'district' are entirely separate; they have no elements in common whatsoever. Conclusion II claims "Some districts are cities," which asserts that there is at least one element common to both sets. This directly contradicts Statement 1.
Therefore, Conclusion II does not follow from the statements.
Evaluating Conclusion III: No state is a zone.
Statement 3 says, "Some zones are states." This is a particular affirmative statement, indicating that there is at least one element common to both the set of 'zones' and the set of 'states'. Conclusion III claims "No state is a zone," which is a universal negative statement asserting that there is no common element between the sets of 'state' and 'zone'. This directly contradicts Statement 3.
Therefore, Conclusion III does not follow from the statements.
Summary of Conclusions
- Conclusion I: Some zones are districts. – Follows (from Statement 2)
- Conclusion II: Some districts are cities. – Does Not Follow (contradicts Statement 1)
- Conclusion III: No state is a zone. – Does Not Follow (contradicts Statement 3)
Based on our analysis, only Conclusion I logically follows from the given statements.
| Conclusion | Evaluation | Reasoning |
|---|---|---|
| I. Some zones are districts. | Follows | Directly implied by Statement 2: "Some districts are zones." |
| II. Some districts are cities. | Does Not Follow | Contradicts Statement 1: "No city is a district." |
| III. No state is a zone. | Does Not Follow | Contradicts Statement 3: "Some zones are states." |
Revision Table: Types of Categorical Propositions
Understanding the different types of statements helps in analyzing logical conclusions. These are based on quantity (universal/particular) and quality (affirmative/negative).
| Type | Form | Example | Quantity | Quality |
|---|---|---|---|---|
| A | All S are P | All dogs are mammals. | Universal | Affirmative |
| E | No S are P | No cats are dogs. | Universal | Negative |
| I | Some S are P | Some students are intelligent. | Particular | Affirmative |
| O | Some S are not P | Some students are not intelligent. | Particular | Negative |
Additional Information: Conversion in Syllogism
Conversion is a type of immediate inference where the subject and predicate terms of a proposition are interchanged. The validity of the conversion depends on the type of proposition:
- A (All S are P): Converts to I (Some P are S). (Valid by limitation)
- E (No S are P): Converts to E (No P are S). (Simple Conversion - Valid)
- I (Some S are P): Converts to I (Some P are S). (Simple Conversion - Valid)
- O (Some S are not P): Does not have a valid conversion.
In this problem, Statement 2 ("Some districts are zones" - I type) converts to "Some zones are districts" (I type), which is Conclusion I. This conversion is valid, confirming that Conclusion I follows.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
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.
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. 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.
