facts. Based solely on the statements, determine which of the conclusions logically follow.
Statements:
All cars are vehicles.
Some vehicles are bikes.
No bike is a truck.
Conclusions:
(1) Some vehicles are not trucks.
(2) No car is a bike.
(3) Some cars are bikes.
(4) Some trucks are vehicles.
Analyze Statements: Cars, Vehicles, Bikes, and Trucks
This problem requires us to analyze the logical relationship between different categories based on a set of given statements. We need to determine which of the provided conclusions necessarily follow from these statements, assuming the statements are true.
Understanding the Statements
Let's break down the information given:
- Statement 1: All cars are vehicles. This means the entire group of 'cars' is included within the larger group of 'vehicles'. If something is a car, it must also be a vehicle. We can represent this as: Cars $\subset$ Vehicles.
- Statement 2: Some vehicles are bikes. This indicates that there is an overlap between the group 'vehicles' and the group 'bikes'. At least one vehicle is also a bike. We can represent this as: Vehicles $\cap$ Bikes $\neq \emptyset$.
- Statement 3: No bike is a truck. This means the groups 'bikes' and 'trucks' are completely separate; they have no members in common. We can represent this as: Bikes $\cap$ Trucks = $\emptyset$.
Conclusion Analysis
Now, let's evaluate each conclusion based solely on these statements:
Conclusion (1): Some vehicles are not trucks.
- From Statement 2, we know that there exist certain vehicles that are bikes.
- From Statement 3, we know that none of these bikes (which are vehicles) can be trucks.
- Therefore, those specific vehicles (the ones that are bikes) are definitely not trucks.
- This means that at least 'some' vehicles are not trucks.
- Conclusion (1) logically follows.
Conclusion (2): No car is a bike.
- Statement 1 tells us all cars are vehicles (Cars $\subset$ Vehicles).
- Statement 2 tells us some vehicles are bikes (Vehicles $\cap$ Bikes $\neq \emptyset$).
- The statements do not specify whether the vehicles that are bikes overlap with the cars. It's possible that the vehicles which are bikes are *not* cars, or it's possible that some cars *are* bikes (since cars are also vehicles).
- Because we cannot be certain based on the given information, we cannot conclude that 'No car is a bike'.
- Conclusion (2) does not necessarily follow.
Conclusion (3): Some cars are bikes.
- Similar to the analysis for Conclusion (2), we know cars are vehicles, and some vehicles are bikes.
- However, the statements do not provide enough information to confirm that the specific vehicles identified as bikes must include any cars. The vehicles that are bikes could potentially be vehicles that are not cars.
- Therefore, we cannot definitively conclude that 'Some cars are bikes'.
- Conclusion (3) does not necessarily follow.
Conclusion (4): Some trucks are vehicles.
- Statement 3 says no bike is a truck.
- Statement 1 says all cars are vehicles.
- Statement 2 says some vehicles are bikes.
- There is no information linking 'trucks' directly or indirectly to 'vehicles' in a way that guarantees an overlap. It is entirely possible for the set of trucks to be completely separate from the set of vehicles, consistent with the given statements.
- For example, vehicles could be {cars, buses, motorcycles} and trucks could be a separate category.
- Therefore, we cannot conclude that 'Some trucks are vehicles'.
- Conclusion (4) does not necessarily follow.
Final Determination
Based on the analysis, only Conclusion (1) logically follows from the given statements. The options provided indicate that the correct choice is the one stating only Conclusion (1) 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. 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.
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.
