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Exercise 4.2 Given two relations R1 and R2, where R1 contains N1 tuples, R2 contains N2

tuples, and N2 > N1 > 0, give the minimum and maximum possible sizes (in tuples) for the

resulting relation produced by each of the following relational algebra expressions. In each

case, state any assumptions about the schemas for R1 and R2 needed to make the expression

meaningful:

(1) R1 U R2, (2) R1 n R2, (3) R1 - R2, (4) R1 x R2, (5) (Ta=5(R1), (6) 7Ta(R1), and

(7) R1/R2

 

Exercise 4.3 Consider the following schema:

Suppliers( sid: integer, sname: string, address: string)

Parts(pid: integer, pname: string, color: string)

Catalog( sid: integer, pid: integer, cost: real)

The key fields are underlined, and the domain of each field is listed after the field name.

Therefore sid is the key for Suppliers, pid is the key for Parts, and sid and pid together form

the key for Catalog. The Catalog relation lists the prices charged for parts by Suppliers. Write

the following queries in relational algebra, tuple relational calculus, and domain relational

calculus:

1. Find the narnes of suppliers who supply some red part.

2. Find the sids of suppliers who supply some red or green part.

3. Find the sids of suppliers who supply some red part or are at 221 Packer Ave.

4. Find the sids of suppliers who supply some rcd part and some green part.

5. Find the sids of suppliers who supply every part.

6. Find the sids of suppliers who supply every red part.

7. Find the sids of suppliers who supply every red or green part.

8. Find the sids of suppliers who supply every red part or supply every green part.

9. Find pairs of sids such that the supplier with the first sid charges more for some part

than the supplier with the second sid.

10. Find the pids of parts supplied by at least two different suppliers.

11. Find the pids of the most expensive parts supplied by suppliers named Yosemite Sham.

12. Find the pids of parts supplied by every supplier at less than $200. (If any supplier either

does not supply the part or charges more than $200 for it, the part is not selected.)