Join or Cross Product

Hi,

Got a problem with a question on a study sheet for my exam next week, can someone please help clear it up? It is *not* homework, term is finished and our summer reading list is on java and C not relational algebra, just in case there's any confusion (I was off ill at the first sitting and missed alot of the course :( ).

The question asks to list the names of employees who have a dependant with the same first name as themselves using relational algebra.

The schema is given below (keys are enclosed in asterixes):

Employee (*NINumber*, Fname, Lname, Address, Sex, Birthdate, Salary, Supervisor, WorksFor)

Department (*Number*, Name, Manager, StartDate)

Project (*Number*, Name, Location, ControllingDept)

Dependant (*ENINumber*, *Name*, Sex, Relationship, Birthdate)

WorksOn (*Emp*, *Proj*, Hours)

Location (*Dnumber*, *Lname*)

Relation Foreign Key Refs Relation Key

Employee	Supervisor	->	Employee	NINumber
Employee	WorksFor	->	Department	Number
Department	Manager		->	Employee	NINumber
Project		ControllingDept	->	Department	Number
Dependant	ENINumber	->	Employee	NINumber
WorksOn		Emp		->	Employee	NINumber
WorksOn		Proj		->	Project		Number
Location	Dnumber		->	Department	Number

ok, down to the main problem...

I started by writing down the main steps in getting the result.

1. Get all the employees who have dependants.
2. Get employees who have dependants with same first name.
3. Get names of those employees.

EmpDependants := select (Employee x Dept, NINumber = ENINumber)
// Get employees of any employees with dependants along with dependant
information.

EmpDepSameName := select (EmpDepends, Fname = Name)
// Get employees who have same first name as their dependant.

EmpNames := project (EmpDepSameName, Fname, Lname)

// Get columns corresponding to employee names.

Firstly, is this correct and secondly what happens if instead of using the cross product a join is used? i.e.

EmpDependants := join (Emp, NiNumber, Dependant, ENINumber)

Is there a difference in this circumstance?

Thanks,
Chris

p.s. the schema and requirements (in a separate document) are not at all clear on whether the dependants name is only their first name or includes the whole dependant name. No indication was given if we were allowed other functions beyond those given (I don't see why not), so I assumed for the purpose of the question that the dependant name was only their first name.

-- 
for personal replies change 'spamoff' to 'chris'