Comet Coffee $($CC$)$ is a new coffee shop franchise that is starting to gain in popularity. As part of its growing pains, it needs help when it comes to designing databases. Below is a randomly selected sample listing showing different product sales. As a newly assigned database architect, you realize this current single list will break down as the firm grows with more products, locations and sales. Your task is to determine a better approach to handling CC$$s data needs, using database normalization practices. To achieve your goal, answer in order the questions shown below.

$1.$ Assuming that all functional dependencies are apparent in this data, which of the following are true? Highlight the answer row$($s$).$

a$.($ProductID$)->($ProductName$,$StoreLocation$)$

b$.($ProductID$,$ UnitPrice$)->($ProductName$,$QtySold$)$

c$.($CashierID$)-->($StoreID$)$

d$.($StoreID$)-->($CashierID$)$

e$.($StoreID$,$ OrderID$)-->($StoreCategory$,$ StoreLocation$)$

f$.($ProductID$)->($ProductType$,$ProductName,UnitPrice,UnitCost$)$

g$.($ProductID$,$ ProductType$)->($ProductName$,$UnitPrice,UnitCost$)$

h$.($OrderID$,$ ProductID$)->($OrderDate$,$ CashierID, QtySold,UnitPrice$)$

i$.($OrderID$,$ OrderDate, CashierID$)->($QtySold$,$UnitPrice, ProductID, StoreID$)$

j$.($StoreID$)-->($StoreCategory$,$ StoreLocation$)$

$$

$2.$ Assume a PRODUCT entity can be derived from the above listing. List all candidate keys for PRODUCT. Restrict your answer to the row$($s$)$ you highlighted in #$1.$

$3.$ Based on your answer to #$2,$ which candidate key would make the better primary key of the PRODUCT entity? List your reasoning.

$4.$ Are any determinants you highlighted in #$1$ not a candidate key of the PRODUCT entity? If so$,$ list those functional dependency$($ies$),$ in standard notation

$5.$ Based on what you determined in questions $3$ and $4,$ and considering future growth, is it necessary to split the provided sample data matrix into multiple entities? If so$,$ list the themes of all entities.

$6.$ For each theme identified in question #$5,$ use standard entity$/$relation notation $[$i$.$e$.$ ENTITY$\_$NAME $($PrimaryKey$,$ Column$02,$ Column$03,...,$ ForeignKey$)]$

to describe each entity. Identify all primary and foreign keys. Hint: If any attribute in an entity $($Entity A$)$ is part of a primary key for A and also serves as a foreign key to another entity $($Entity B$),$ you would both underline and italicize the attribute$($s$)$ in A$$s notation. List any assumptions.