E$4\mathrm{.}9$ Consider the following relation with sample data.

HEALTH CENTER TABLE

$\backslash$table$[[$ DocID ${?}_{(}),$DocName, PatientID ${?}_{(}),$PatientName,InsuranceCoID,InsuranceCoName,NextAppointmentDate$],[1,$Dr$.$ Joe,$111,$Max,$11,$ACME Insurance,$1-$Dec$],[1,$Dr$.$ Joe,$222$ U$,$Mia,$11,$ACME Insurance,$2-$Dec$],[1,$Dr$.$ Joe,$333,$Pam,$12,$Purple Star,$3-$Dec$],[2,$Dr$.$ Sue,$333,$Pam,$12,$Purple Star,$7-$Dec$],[3,$Dr$.$ Kim,$555,$Lee,$13,$Tower Block,$2-$Dec$],[3,$Dr$.$ Kim,$111,$Max,$11,$ACME Insurance,$3-$Dec$],[4,$Dr$.$ Joe,$666,$Alen,$14,$All Protect,$9-$Dec$]]$

The HEALTH CENTER Table captures the data about patients' appointments with doctors.

Each patient has a unique Patient ID and a Patient Name.

Each doctor has a unique Doc ID and a Doc Name.

Each patient has one insurance company.

Each insurance company has a unique Insurance Co ID and Insurance Co Name.

Each appointment is scheduled between one patient and one doctor.

Each patient can have many appointments scheduled $($but only one appointment scheduled with one particular doctor$).$

E$4\mathrm{.}9$a Depict full key functional dependencies, partial functional dependencies $($if any$),$ and transitive functional dependencies $($if any$)$ in the Health Center Table.

E$4\mathrm{.}9$b Show the result of normalizing the Health Center Table to $2$NF$.$

E$4\mathrm{.}9$c Show the result of normalizing the Health Center Table to $3$NF$.$