Solving 'All' like problems in SQL (DB)

The typical problem:
Display the .... of all... that have ....
Display the ..yR1.. of all...R2.. that have ....

Using Relation algebra the R1 / R2 = ProjY(R1) - ProjY { ProjY(R1) x R2 - R1 )

R1(a,b) R2(b)

Display the name a which consist of all b that have ....

ProjY(R1) - ProjY { ProjY(R1) x R2 - R1 )
........................^----------------^ ----------------Max possible result (a x b)
........................^----------------------^ ----------Result that do not qualify
..............^---------------------------------^ ---------Extract a that do not qualify
^-----------------------------------------------^ ---------Extract a that qualify

[1]Using SQL an example:

Supplier(S#,SName,City)
Part(P#,PName,Color,Weight,City)
Supplies(S#,P#,Qty)

Get supplier names for suppliers who supply ALL parts


SELECT DISTINCT S.SNAME
FROM S
WHERE NOT EXSITS
( SELECT *
FROM P -------------------->ALL Parts
WHERE NOT EXISTS
( SELECT *
FROM SP
WHERE SP.S# = S.S#
AND SP.P# = P.P# ---------------->Existing parts) ) ------>Unqualified parts

[2]Using SQL an example:

Find all Borrowers who have an member account at all Library branches located in
Singapore.

account (account_number, branch_name, numbooks)
branch (branch_name, branch_city, assets)
Lib_Member (borrower_name, account_number)

select distinct S.borrower_name
from Lib_Member as S
where not exists (
(select branch_name
from branch
where branch_city = ‘Singapore’--------------> All possible branch)
except----------------------------->Subtracted branch quality
(select R.branch_name--------------->Branch that may or may not qualify
from Lib_Member as T, account as R
where T.account_number = R.account_number and
S.borrower_name = T.borrower_name ))


Other unrelated SQL an example:

Given:

teaching(prof_id, crs_code, term)
professor(prof_id, name, dept_id)

Display the names of all professors that have taught both 291 and 391 but have
never taught 229.

Solution:
SELECT name
FROM professor p,
((SELECT prof_id as pid
FROM teaching
WHERE crs_code = '291'
INTERSECT
SELECT prof_id as pid
FROM teaching
WHERE crs_code = '391'
)
EXCEPT
SELECT prof_id as pid
FROM teaching
WHERE crs_code = '229'
) as t
WHERE p.prof_id = t.pid