Consider a relational database with the following relations:

Managers $($Name$,$ Dep$)$

Departments $($Name$,$ Location, Manager$)$

Works$-$For $($Dept$\_$Name, Emp$\_$ID$)$

Employees $($ID$,$ Name, Salary$)$

Here, Managers contains a tuple for each manager, recording its name and the

department managed. Departments contains a tuple for each department, recording

its name and location. Employees records the ID$,$ name, and Salary of the

employees. Works$-$For keeps track of the relationship between Departments and

Employees.

Please provide tuple relational calculus and domain relational calculus queries for

the queries stated in English in questions $10$a$-10$c below:

$10$a$.(2$ points$)$ Retrieve the name of all employees who work in the $$Marketing$$

department$\mathrm{.}7$

$10$b$.(2$ points$)$ Retrieve the name of the manager along with the number of

employees who manage and work respectively in the $$Engineering$$

department in ascending order of employee ID$.$

$10$c$.(2$ points$)$ Retrieve the name of the employee$($s$)$ who earned the most in each

department that has more than $50$ employees.

$10$d$.($Optional Extra Credit$)$ Express the following SQL statement using both the

relational and domain calculus notations?

SELECT UNIQUE$($d$.$number$)$

FROM departments d$,$ employees e$,$ works$\_$for w

WHERE w$.$name $=$ d$.$name AND

w$.$Emp

$\_$

ID $=$ e$.$ID AND

d$.$name $=$Sales$$