Writing SQL query equivalent to relational division of relational algebra? These are the list of 3 tables

EMPLOYEE (Ssn#, Fname, Lname, Bdate, Address, Sex, Salary, Super_ssn)

WORKS_ON (Essn#, Pno, Hours)

PROJECT (Pnumber#, Pname, Plocation)


Question 1: Write SQL query (equivalent to relational division of relational algebra) to retrieve the project name which is contributed by all employees

Question 2: Write SQL query (equivalent to relational division of relational algebra) to retrieve the first name and last name of all employees who work on every project

Then there are list of 6 tables

ITEM (Item#, Item_Name, Unit_Price)

ORDER (Order#, Ord_Date, Cust#, Ord_Amt)

ORDER_ITEM (Order#, Item#, Qty)

WAREHOUSE (Warehouse#, Warehouse_City)

SHIPMENT (Order#, Warehouse#, Ship_Date)

WAREHOUSE_ITEM (Item#, Warehouse#, Qty)


Question 3: Write SQL query (equivalent to relational division of relational algebra) to list Item_Name and Quantity that are stored in all warehouses in Sydney

All these 3 questions are assignment questions.
However, I have tried and answered them and which is shown below:

Answer for Question 1:

SELECT Pname 
FROM PROJECT
WHERE EXISTS (SELECT Pname 
              FROM PROJECT, EMPLOYEE 
              WHERE PROJECT.Pnumber = WORKS_ON.Pno);


Answer for Question 2:

SELECT Fname, Lname 
FROM EMPLOYEE
WHERE EXISTS (SELECT Fname, Lname 
                            FROM EMPLOYEE, WORKS_ON, PROJECT
                            WHERE EMPLOYEE.Ssn = WORKS_ON.Essn 
                              AND WORKS_ON.Pno = PROJECT.Pnumber);


Answer for Question 3:

SELECT Item_Name, Qty 
FROM ITEM, ORDER_ITEM
WHERE ITEM.Item# = ORDER_ITEM.Item#
  AND EXISTS(SELECT * 
             FROM WAREHOUSE 
             WHERE Warehouse_City = 'Sydney');


I just want to confirm that if my SQL query logic for these 3 questions are correct or not.

If it is correct, then I will able to proceed and convert them in relational algebra with relational division which I can do it by myself if my SQL query logic is correct.

If it is not correct, then kindly correct the mistakes in my SQL query logic wherever applicable which would be very helpful for me.
The third seems correct.  The first and second strike me as wrong.  You are looking for projects where any employee contributed, not where all contributed.  In essence you are doing a division on an ANY rather than an ALL criteria.

In these cases you need to change your queries to use NOT EXISTS and look for mismatches.