Three statements are given, followed by four conclusions numbered I, II, III and IV. 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: Some cars are bikes.All bikes are trucks.Some trucks are buses. Conclusions: I. Some trucks are cars. II. All buses are cars. III. Some cars are buses. IV. All bikes are buses.
- AOnly conclusion I follows
- BOnly conclusions I and IV follow
- COnly conclusions II and III follow
- DOnly conclusions I, II and IV follow
Solution & Step-by-step Explanation
Let's analyze the statements using Venn intersections: Statement 1: Some cars are bikes. (Overlapping between Cars and Bikes)Statement 2: All bikes are trucks. (The entire Bike circle is inside the Truck circle)Since some cars are bikes, and all bikes are trucks, the part of cars that is bike must also be truck. Therefore, there is a guaranteed overlap between Trucks and Cars.Statement 3: Some trucks are buses. (Overlapping between Trucks and Buses)Now let's evaluate the conclusions:Conclusion I: Some trucks are cars.As shown above, the intersection between Cars and Trucks is guaranteed. This conclusion follows.Conclusion II: All buses are cars.There is no mandatory relationship given that forces all buses to be inside cars. This does not follow.Conclusion III: Some cars are buses.Buses overlap with Trucks, but they do not necessarily have to touch the Car circle. This does not follow.Conclusion IV: All bikes are buses.Bikes are inside Trucks, and some trucks are buses, but this does not imply that all bikes are buses. This does not follow.Hence, only conclusion I follows.