Task $3(3\mathrm{.}0$ marks$)$ Analysis of business statements and normalization

Each manufacturer manufactures many disk$-$drives, and the manufacturer assigns each disk$-$drive a serial number. The serial number is unique within a manufacturer, but not across all other manufacturers. The manufacturer registers the model of the disk$-$drive it produces to the intellectual property Office of Singapore $($IPOS$)$ so that the model of the disk drive is protected and cannot be used by other manufacturer. The disk$-$drives are manufactured by batch, and all the disk$-$drives manufactured in a batch are of the same model, and all the diskdrives of the same model have the same capacity. A distributor collaborates with many manufacturers to help the manufacturers to distribute the disk$-$drives the distributor receives to retailers. A distributor creates a relational table DISK$\_$DRIVE to store the information$/$attributes of the disk drive it distributes to retailers as follows:

DISK$\_$DRIVE$($serialNum$,$ manufacturer, model, batch, capacity, retailer$)$

Each tuple in the relation DISK$\_$DRIVE contains information about a disk drive with a unique serialNum, made by a manufacturer, with a particular model number, released in a certain batch, which has a certain storage capacity and is sold by a certain retailer. For example, the tuple Disk$\_$drive$(\text{'}1978649\text{'},$ 'WesternDigital', $\text{'}$A$2235$X$\text{'},\text{'}765234\text{'},500,$ 'CompSingapore'$)$ specifies that WesternDigital made a disk drive with a serial number $1978649$ and a model number A$2235$X$,$ released in batch $765234$ ; it is $500$ GB and is sold by CompSingapore.

Write each of the following statements as a function dependency:

i$.$ The manufacturer and serial number uniquely identify the drive.

ii$.$ A model number is registered by a manufacturer and therefore cannot be used by another manufacturer.

iii. All disk drives in a particular batch are the same model.

iv$.$ All disk drives of a certain model of a particular manufacturer have exactly the same capacity.