Consider the following schema:

SUPPLIERS (SID: integer(pk), SNAME: string, STREET: string, CITY: string, ZIP: string) PARTS (PID: integer(pk), PNAME: string, COLOR: string) CATALOG (SID: integer(pk), PID: integer(pk), COST: real)

The primary key attributes are underlined, and the domain of each attribute is listed after the attribute name. Thus, SID is the primary key for SUPPLIERS, PID is the primary key for PARTS, and SID and PID together form the primary key for CATALOG. Attribute SID in CATALOG is a foreign key that refers to the primary key SID of SUPPLIERS and PID in CATALOG is a foreign key that refers to the primary key PID of PARTS. The CATALOG relation lists the prices charged for parts by suppliers.

Write the following queries in relational algebra.

10. Find the PIDs of parts supplied by every supplier who supplies at least one part.

11. Find the SIDs of suppliers who supply at least two different parts (you are not allowed to use a grouping/aggregation operation for this query).

12. Find the SIDs of suppliers who supply at least two different parts (you have to use a grouping/aggregation operation for this query).

13. For every part, find its PID, its PNAME and the number of suppliers who sell it.

14. List the PID, PNAME and average cost of all parts.

15. Find the average cost of red parts.

16. Find the average cost of parts supplied by suppliers named 'Yosemite Sham'.