$4-58.$ A bus company is responsible for offering public transportation in the suburbs of a large metropolitan area. The company has significant data management requirements: It needs to keep track of its $150$ vehicles, $400$ drivers, $60$ bus routes, and hundreds of scheduled departures every day. In addition, it is essential for the company to know which drivers are certified to drive which buses.

The data that the company has available include the following attributes:

RoutelD, RouteStartPoint, RouteEndPoint, RouteStandardDrivingTime, ScheduleDate, ScheduledDepTime, ScheduledArrTime, DriverID, DriverFName, DriverLName, DateDriverJoinedCompany, DriverDOB, VehicleID, VehicleMake, VehicleModel, VehiclePassangerCapacity, DriverCertStartDate, DriverCertEndDate.

Sample data for this set of attributes are as follows:

$28,$ Grand Avenue, Madison Street, $38,\{9/12/2021,8\mathrm{.}30,9\mathrm{.}18,8273,$ Mary, Smith, $5/2/2007,3/23/1974,1123,$ GreatTrucks, CityCoach, $58,6/10/2021,6/9/2022$ I $9/12/2021,9\mathrm{.}30,10\mathrm{.}12,7234,$ John, Jones, $10/12/2011,12/15/1991,5673,$ GreatTrucks, CityCoach $2,62,4/12/2021,4/11/2022$ I $9/12/2021,10\mathrm{.}30,11\mathrm{.}08,2343,$ Pat, Moore, $2/24/1982,1/19/1958,4323,$ PowerTransport, MidiBus, $32,8/20/2021,8/19/2022\}$

Note that the information for specific bus schedules $($starting with the attribute ScheduleDate$)$ is repeated three times in the sample data set and is separated by the "I" symbol. Also, take into account that in this case, the certification is specific to a particular vehicle driver pair.

Based on the facts stated above,

a$.$ Identify the functional dependencies between the attributes.

b$.$ Identify the reasons why this set of data is not in $3$ NF and indicate the normal form $($if any$)$ it is in$.$

c$.$ Including all intermediate stages, organize the attributes into a set of $3NF$ relations.