Specify the following queries in relational algebra on the database schema in Exercise 5.17:

a. For the salesperson named ‘Jane Doe’, list the following information for all the cars she sold: Serial#, Manufacturer, Sale_price.

b. List the Serial# and Model of cars that have no options.

c. Consider the NATURAL JOIN operation between SALESPERSON and SALE. What is the meaning of a left outer join for these tables (do not change the order of relations)? Explain with an example.

d. Write a query in relational algebra involving selection and one set operation and say in words what the query does.

Exercise 5.17

Consider the following relations for a database that keeps track of automobile sales in a car dealership (OPTION refers to some optional equipment installed on an automobile):

CAR(Serial_no, Model, Manufacturer, Price)

OPTION(Serial_no, Option_name, Price)

SALE(Salesperson_id, Serial_no, Date, Sale_price)

SALESPERSON(Salesperson_id, Name, Phone)

First, specify the foreign keys for this schema, stating any assumptions you make. Next, populate the relations with a few sample tuples, and then give an example of an insertion in the SALE and SALESPERSON relations that violates the referential integrity constraints and of another insertion that does not.