Problem 1. Given the following relations (primary keys are underlined):

Emp(eid: integer, ename: string, age: integer, salary: real),

Works(eid: integer, did: integer, pct_time: integer),

Dept(did: integer, dname: string, budget: real, managerid: integer)

Write Relational Algebra expressions for the following questions/queries.

Find employees names and eids for those who works in a dept with a budget larger than $500,000.

Find employees names and eids for those who work in at least two different departments.

Find department names and dids for those departments that have only full-time employees (If pct_time = 100%, the employee is full-time in this department)

Find departments names and dids for those that have only employees with salary larger than $40,000 there.