Consider a database consisting of the following tables:

Person(Pname, Street, City, Cname, Salary) Primary Key :Pname

Company(Cname, City, Sales) Primary Key :Cname

Branch(Cname, City) Primary Key: Cname, City

The Person relation provides the information about a person including the name, address(street and city), the company for which the person works, and his/her salary. The Company table provides the city in which the company is headquartered plus the company's total sales. The Branch relation provides the cities in which the company has branches (might be different than HQs city).

Write expressions in Relational Algebra(RA), to retrieve answers to each of the following queries. Also, write queries in Tuple Relational Calculus(TRC) that retrieve the answers to the first three queries.

1. Find the names of all companies that have a branch in every city where Facebook also has a branch.

2. Find the names of companies headquartered in Chicago which have at least two branches in two different cities.

3. Find pairs of company names (i.e., (C1,C2)) in which both companies are headquartered in Chicago and the sales of the first company (i.e.,C1) is higher than the sales of the second company (i.e., C2).