Suppose we have a relation Employees (SSN, name, department, salary).
For each of the following queries, either write the query in relational algebra and explain informally why your answer works, or explain why it cannot be written in relational algebra.
You may use sequences of assignments or expression trees if you like. You may use only the following operators of relational algebra: union, intersection, difference, selection, projection, products, joins (theta and natural), renaming.
a) Find all department(s) with at least two employees of different names.
b) Find the department(s) with the most people.
c) Find the names of employee(s) with the highest salary.
d) For each employee, find their name and their supervisor's name.
e) Find the supervisor with the lowest salary
f) Find the number of supervisor in every department.