Relational Algebra

The schema of a table describes the structure of the table, including the names and types of its columns. Here are the schemas for the tables.

Department $($DName$,$ DNumber, MgrSSN$,$ MgrStartDate$)$ Dept$\_$Locations $($DNumber$,$ DLocation$)$

Employee$($FName$,$ MName, LNamne, SSN$,$ BDate, Address, Sex, Salary, SuperSSN $($Supervisor$$s

SSN$),$ DNo$)$

DEPENDENT$($ESSN$,$ Dependent$\_$Name, Sex, BDate, Relationship$)$ PROJECTS$($PName$,$ PNumber, PLocation, DNum$)$ WORKS$\_$ON$($ESSN$,$ PNo, Hours$)$

Using relational algebra, answer the following questions.

$1.$ List the names of employees in department $5$ who work more than $10$ hours per week on the ProductX project. $($Hint: simple Select$-$Project$-$Join query$)$

$2.$ List the names of employees who have a dependent with the same first name as themselves. $($Hint: simple Select$-$Project$-$Join query$)$

$3.$ List the names of employees who are directly supervised by Franklin Wong. $($Hint: select$-$ project$-$self$-$join query$)$

$4.$ List the names of employees who work on every project. $($Hint: Divide query$)$

$5.$ List the names of employees who do not work on any project. $($Hint: use minus$)$

$6.$ List the names and addresses of employees who work on at least one project located in Houston but whose department has no location in Houston. $($Hint: Use intersect for the "but" and minus for the second criterion$)$

$7.$ List the names of department managers who have no dependents. $($Hint: Use minus$)$

$8.$ List the names of employees whose supervisor's supervisor has a social security number of $888665555.($Hint: self$-$join twice!$)$

$9.$ List the name$($s$)$ of employee$($s$)$ with the lowest salary. $($Hint: Since we do not have aggregate operation min, you can use find the employees that are NOT the lowest in salary and then use minus$)$

$10.$ List the names of employees who work in the department that has an employee with the highest salary among all employees. $($Hint: similar to previous!$)$