Q$3.$B: 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. Write the following queries in relational algebra. $(6$ marks$)$

$($a$)$ Find the names of suppliers who supply some red part.

$($b$)$ Find the sids of suppliers who supply some red or green part.

$($c$)$ Find the sids of suppliers who supply some red part or are at $221$ Packer

$($d$)$ Find the sids of suppliers who supply some red part and some green part

$($e$)$ Find the sids of suppliers who supply every part.

$($f$)$ Find the sids of suppliers who supply every red part.