$(20$ points$)$ Consider the following schema for a database that keeps the information

about business trips and their associated expenses by employees:

EMPLOYEE $($SSN$,$ Name, DeptNo, JobTit$7$e$,$ Salary$)$

TRIP $($TripId$,$ DepartureCity, DestinationCity, DepartureDate, ReturnDate, SSN$)$

A

EXPENSE $($TripId$,$ Item, Date, Amount$)$

a$.$ Get a list of all the different destination cities where the employees have taken

trips.

b$.$ Find all the employee information for employees who work in Department $4.$

c$.$ Get complete trip records $($but not their associated expenses$)$ for all trips with

departure dates after July $1$ of the current year.

d$.$ Find the names of all employees who have departed on trips from Shanghai.

e$.$ Find the SSN of all employees who have any single expense item of more than

$$1500$ for any trip.

f$.$ Find the names of all employees who have any expense item with value

"Entertainment."

g$.$ Find the destination cities of all trips taken by employees who have the job title of

"Manager".

h$.$ Find the names and departments of all employees who have a single expense item

of over $$500$ since January $1$ of this year.

i$.$ Find the items and amounts of all expenses for a trip to Cairo beginning on

January $10$ of this year taken by employee Jane.

j$.$ Find the names, departments, and job titles of all employees who have any expense

item with value "Service Charge" for trips taken to NYC last year, along with the

date and amount of the expense.

$(6$ points$)$ Take into consideration the following schema and write the Relational Algebra

statement for the following:

Manufacturer $($mid$,$ name, address$)$

Supplies $($mid$,$ pid$)$

Parts $($pid$,$ partname, color$)$

a$.$ Find the names of Manufacturers who supply some blue part.

b$.$ Find the mids of Manufacturers who supply some red part and some black part.

$(4$ points$)$ Consider a schema with two relations, $R(A,B)$ and $S(B,C),$ where all values

are integers. Make no assumptions about keys. Consider the following three relational

algebra expressions:

a

b$){}_A({}_B=1R){}_c({}_B=lS)$

c$){}_{A,C}({}_A,R{}_B=1S)$

Two of the three expressions are equivalent $($i$.$e$.$ produce the same answer on all

databases$),$ while one of them can produce a different answer. Which expression can

produce a different answer?