Consider the following relational schema:

emp$($eid:integer, ename:string, age:integer, salary:real$)$

works$($eid:integer, did:integer, pc time:integer$)$

dept$($did:integer, dname:string, budget:real, managerid:integer$)$

The underlined attributes are keys for their relations. Note that a manager is an employee as well

and their manager id and employee id are the same. An employee can work in more than one

department. The pct time field of the works relation shows the percentage of time that a given

employee works in a given department and is always greater than zero.

A sample database $($sample db$.$sql$)$ is provided with this assignment and the output of the correct

queries over this sample database is given in each part of this question. You may use this sample

database to test or debug your queries. We have created an account for each student on the

MySQL server of our department. The access guide to the MySQL server

$($database access guide.txt$)$ is also posted with this assignment. You can import the sample

database to your account on the MySQL server and use it to ensure that your queries are correct.

Notice that your SQL queries must return the correct result over every possible database instance

of the aforementioned schema for the questions and not only over the sample database.

You should not submit any $.$sql file in your assignment submission and must write your final SQL

queries in a single PDF file that you submit for all questions in this assignment.

Write the queries in parts $($a$)$ and $($b$)$ using relational algebra, nonrecursive Datalog, relational

calculus, and SQL$.$ Write the rest of queries only in SQL$.$