USE RELATIONAL ALGEBRA! I WILL THUMBS UP$!$ Consider the following schema of a Company database: Assignment $1\mathrm{.}5(15$ marks$)$

Return the eid of the Employees who are working for the maximum number of Departments.

Assignment $1\mathrm{.}6(15$ marks$)$

Return the pid of the Projects that have the minimum budget.

Assignment $1\mathrm{.}7(15$ marks$)$

Return the pids of the Projects for which at least two different Employees are working.

Assignment $1\mathrm{.}8(10$ marks$)$

Union and Set Difference are among the five basic RA operations, but Intersection is not. Show how

to implement Intersection using Union and Set Difference.

Employees $($eid: integer, ename: string, address: string,

supereid: integer, salary: integer$)$

Departments$($did: integer, dname: string$)$

Projects$($pid: integer, pname: string, did: integer, budget:

integer$)$

Works$\_$on$($eid: integer, pid: integer, hours: integer$)$

Primary keys are underlined. Each Employee has a supervisor $($another Employee$)$ referenced by their

supereid. Projects are uniquely assigned to a Department. The Works$\_$on relation records which

Employee works on which Project for how many hours a week. The primary key of a relation consists of

all its underlined attributes. There are foreign key constraints between Employees.supereid and

Employees.eid, between Works$\_$on$.$eid and Employees.eid, between Works$\_$on$.$pid and Projects.pid and

between Projects.did and Departments.did.

For assignments $1\mathrm{.}1$ to $1\mathrm{.}7,$ formulate the natural language question as relational algebra $($RA$)$ query

or explain why the query cannot be formulated in RA$.$ You must use the exact notation for the RA

operations introduced in class. In particular, you cannot use dot notation to refer to attributes but must

rename attributes, where necessary.

Assignment $1\mathrm{.}1(10$ marks$)$

For the $"$IT$"$ Department, return the pname of those projects of that Department for which at least one

Employee works.

Assignment $1\mathrm{.}2(10$ marks$)$

For each Employee, return their ename and the ename of their supervisees $($the Employees directly

supervised by that Employee$).$

Assignment $1\mathrm{.}3(10$ marks$)$

For each Employee, return their ename and the ename of the Employees directly or indirectly supervised

by that Employee.

Assignment $1\mathrm{.}4(15$ marks$)$

Return the eids of Employees who do not work on every Project.