Consider the following database that will serve as a data source for a "Data Warehouse".

a$)$ Find the $1$FD $(1$st denormalized form$)$ and the $2$FD $(2$nd denormalized form$).$

$1$FD $-$ obtain a poly$-$tree, replicating the tables that are necessary;

$2$ FD $-$ obtain separate trees, replicating the tables as necessary.

Justify the answer.

b$)$ Check whether the triad $($Departments$,$ Employees, Job History$)$ is redundant or not.

Justify the answer.

c$)$ Considering that:

Additives: are attributes that can be added $($added$)$ across all dimensions, e$.$g$.$ sales value

Semi$-$additives: are attributes that can be added $($added$)$ by some dimensions, e$.$g$.$

Non$-$additives: are attributes that cannot be aggregated $($added$),$ e$.$g$.$ price unitary $($use

Average$()$ for example$)$

No facts: there are only identifiers $($use the Count$()$ function for identifiers$).$

For the fact tables found, define the additive, semi$-$additive, non$-$additive and non$-$fact

attributes. Justify the answer.

d$)$ Then, define a DataWharehouse, in star or constellation, with at least three dimensions

for each fact table.