Relational Algebra
The database used for this question is a very simple one with the following schema: (Primary keys are bold, foreign keys are underlined)

CUSTOMER (CustID, FirstName, LastName, City, Phone, Email)
INVOICE (InvoiceNumber, CustID, Date)
INVOICE_ITEM(InvoiceNumber, ItemNumber, Quantity)
ITEM (ItemNumber, ItemName, UnitPrice)

When a customer makes a purchase, an invoice is created. The invoice may be for many items. For example, in a single purchase, a customer might buy 10 Back Scratchers, 4 Hair Removers and a Dog Lead.

Provide relational algebra (NOT SQL) queries for the following:

a. List the first and last names of Customers who come from the City named Perth.
b. List the first and last names of customers who had transactions on 1st August 2012.
c. List the price of the item called "Back Scratcher"
d. List the first and last names of any customer who has purchased more than 10 "Back Scratchers" in a single transaction.
e. List the names and quantities of items purchased on 1st August 2012 by the customer Peter Griffin.
f. List the dates on which Peter Griffin made purchases.
g. List the first and last names of customers who have bought "Back Scratcher" or "Hair Remover"
h. List the first and last names of customers who have bought "Back Scratcher" but have not bought "Hair Remover"
i. List the first and last names of customers who have bought "Back Scratcher" and "Hair Remover"
j. List the first and last names of any customers who have bought all of the items. (This does not need to be as part of a single purchase).