How to provide relational algebra for the given schema?

Question

EMPLOYEE(PERSONNAME, STREET, CITY)

WORKS(PERSONNAME,COMPANYNAME, SALARY)

COMPANY(COMPANYNAME, CITY)

MANAGES(PERSONNAME, MANAGERNAME)

Find the

Answer 1

As @wildplasser pointed out: The first part of the assumption

assuming that all people work for exactly one company...

declares the case that there is a exact one relation between employees and companies. This would imply that it is not allowed to have data records where an employee is not associated to any company. That is where the second part of the assumptions kicks in

... and people are allowed to appear in the database (e.g. in employee) but not appear in works

So this tells us that is even possible to hold employees not being associated to any company.

For me now i would conclude that the question asks for the zero or one relation between company and employee entities.