Given the relational schema

PATIENTS $=($PatientName$,$ Doctor, DoctorSpecialty, PatientGender, insurance$)$

where all the attributes are atomic, $($PatientName$,$ Doctor, PatientGender$)$ is the only candidate key of PATIENTS, and Doctor

DoctorSpecialty.

Answer the two following questions $($a$)$ and $($b$)$:

a$)$ Explain why PATIENTS does not satisfy the third normal form $(3$NF$)$ with respect to the set of functional dependencies that hold on PATIENTS. Show your work.

b$)$ Use the decomposition algorithm discussed in class to decompose PATIENTS into a set of schemas such that each resulting schema is in $3$NF; show your work. For each resulting schema, give its candidate keys and its complete set of non$-$trivial functional dependencies. You must explain in detail why EACH of your resulting schemas is in $3$NF