Based on the relational schema below: Emp(eid: integer, ename: string, age: integer, salary: real)
Works(eid: integer, did: integer, pcttime: integer)
Dept(did: integer, dname: string, budget: real, managerid: integer)
Express the following queries in Relational Algebra. Please make use of the aggregate relational algebra operators that was explained in class. If you believe you cannot express a given query in relational algebra, explain why not. Or if you end up making some additional assumptions in order to express the queries using relational algebra, please state your assumption clearly.

Required:
a. Find the names and ages of each employee who works in both the Hardware department and the Software department (assume that Hardware Dept ID =0 and Software Dept ID = 1).
b. Find the mamagerids of managers who manage only departments with budgets greater than $1,000,000. Please note that if a manager manages dept 1 and dept 2 and dept 1 has a budget of 2,000,000 and dept 2 has a budget of 10,000, then the manager would not be included in the result list.
c. For each department with more than 20 full-time-equivalent employees (i. e., where the part-time and full-time employees add up to at least that many full-time employees), find the did together with the number of employees which work in that department.
d. Find the name and age of the oldest employee in each department.
e. Find the department with the highest average age of employees.