A database for a company needs to store data about employees, projects,

managers, and secretaries$.$ Each employee is assigned a unique emp$\_$ID and the name of each employee

needs to be recorded. Each project is assigned a unique prj$\_$ID and the budget for each project needs

to be recorded. Multiple employees can participate in a project and an employee may participate in

multiple projects. There is exactly one manager for each project, but a manager may be in charge

of multiple projects. Each manager has exactly one secretary$,$ but a secretary may assist multiple

managers. Managers and secretaries are employees of the company.

$($a$)(15$ points$)$ Draw an E$/$R diagram that captures all of the above requirements.

$($b$)(15$ points$)$ Define tables using SQL that correspond to the E$-$R diagram in $($a$).$ You must

define the smallest number of tables while ensuring that these tables are in BCNF $($you do

not need to prove that the resulting tables are in BCNF$).$ For each table, specify the primary

and foreign keys. Also, add integrity constraints if needed.

$($c$)(10$ points$)$ List all of the nontrivial functional dependencies that you can find from the tables in

$($b$).$ If there are attribute names that are newly introduced in $($b$),$ you may use these names.

Please omit functional dependencies that are redundant $($for example, if a $->$ b is included, do

not add ac $->$ bc$).$