Consider the following medication table with sample data of a hospital that provides information on medicines to be taken by patients:

MEDICATION

$\backslash$table$[[$PatNo$,$PatName,DocID,DocName,MedID,MedName,UWeight,Dosage,TWeight$],[$P$0005,$Isaac,D$002,$Jack,$\backslash$table$[[$M$011],[$M$002],[$M$003]],\backslash$table$[[$Lipitor$],[$Nexium$],[$Plavix$]],\backslash$table$[[4],[3],[5]],\backslash$table$[[2],[3],[2]],\backslash$table$[[8],[9],[9],[10]]],[$P$0012,$Aries,D$005,$Gogo,$\backslash$table$[[$M$001],[$M$011],[$M$003]],\backslash$table$[[$Actos$],[$Lipitor$],[$Plavix$]],\backslash$table$[[7],[4],[5]],\backslash$table$[[2],[3],[1]],\backslash$table$[[14],[12],[5]]],[$P$0013,$Zoe,D$008,$Wang,M$011,$Lipitor,$4,4,16],[$P$0022,$Athena,D$015,$Fisher,M$012,$Crestor,$10,5,50],[$P$0025,$Tracy,D$002,$Jack,$\backslash$table$[[$M$011],[$M$001],[$M$002]],\backslash$table$[[$Lipitor$],[$Actos$],[$Nexium$]],\backslash$table$[[4],[7],[3]],\backslash$table$[[1],[2],[3]],\backslash$table$[[4],[14],[9]]]]$

Where

PatNo $=$ unique patient number;

DocID $=$ doctor $ID$;

MedID $=$ medicine $ID$;

UWeight $=$ weight $of$ one unit $of$ the medicine;

TWeight $=$ total weight $of$ the medicine $tobe$ taken.

PatName $=$ patient name;

DocName $=$ doctor name;

MedName $=$ medicine name;

Dosage $=$ units of the medicine to be taken;

Assumptions:

Each patient has a name and a unique patient number.

Each doctor has a name and a unique doctor ID$.$

Each patient is assigned one doctor to look after him$/$her$.$ All doctors have patients.

Each patient can be assigned to take several medicines but not all patients need to take medicine. There may be some medicines not assigned to be taken by any patient.

Each medicine has a name, a unit weight and a unique medicine ID$.$

$($a$)$ Normalise the MEDICATION relation to the third normal form $(3$NF$).$ Show ALL your steps from UNF to $3NF$ by listing all the relations in UNF, $1NF,2NF$ and $3$NF$.$ Underline your answer's primary key attribute$($s$)$ for each relation. Explain your work in each step.

$($b$)$ Draw an entity relationship diagram to represent the normalised relations in $3NF$ based on the given assumptions. Ensure all entities are labelled and relationships are drawn with the correct symbols