Exercise $2(30\%)$

Consider the following relational database schema, which describes information about shares that can

be owned by employees of companies. Specifically, the database schema consists of: $($a$)$ the relational

schema Employee, in which the attribute cid is a foreign key to the relational schema Company, and

the managerid, which is a foreign key in the same schema, i$.$e$.$ Employees; eid is the primary key of

Employees $($b$)$ the relational schema Company that holds information about companies, in which the

primary key is cid, and $($c$)$ the relational schema Shares that stores information about employees that

have shares of companies, as well as the number of these shares, sharenum; eid in Shares is a foreign

key to Employees, and cid in Shares is a foreign key to Company.

Employee $($eid$,$ cid, salary, managerid$)$

Company $($cid$,$ companyname, location$)$

Shares $($eid$,$ cid, sharenum$)$

Express in relational algebra the following queries:

A$.(6\%)$ Find the eid of employees of the company named 'Google' that have more than $500$ shares

of the company named 'Facebook'.

B$.(6\%)$ Find the eid of employees, the managers of whom have shares in the company that the

former $($i$.$e$.$ the employees$)$ work for.

C$.(9\%)$ Find the eid of employees that have shares from at least $3$ different companies.

D$.(9\%)$ Find the employees that have shares from all the companies stored in the database.