Final answer:
Non-trivial functional dependencies for the route relation likely include 'Route → Destination' and 'Route, Destination → Distance', indicating that the route determines the destination, and a combination of the route and destination determines the distance. Validity should be checked against real-world data.
Step-by-step explanation:
The question pertains to identifying non-trivial functional dependencies in a given relation called route. A non-trivial functional dependency in database terminology signifies a relationship where a set of attributes can determine other attributes uniquely, without it being a mere reflection of the attributes themselves.
To list all non-trivial functional dependencies, we must understand that:
- a. Route → Destination implies that the route uniquely determines the destination.
- b. Route, Destination → Distance indicates that a combination of the route and destination uniquely determine the distance.
- c. Distance → Route, Destination would mean that the distance could determine both the route and destination, however, this is highly unlikely as multiple routes can have the same distance.
- d. Destination → Route implies the destination uniquely determines the route, which can also be impractical as there can be multiple routes leading to the same destination.
Considering the realistic scenarios of routing and destinations, the most likely non-trivial functional dependencies from the given options are 'a' and 'b', provided routes are uniquely defined and each route has a single defined destination and distance to it. However, it's important to validate these functional dependencies with real-world data.