SQL Division using 'not exists' in mysql

Question

I have the following table:

'committee' table

commname    profname
========================
commA    bill
commA    jack
commA    piper
commB    bill
commB    piper

and I am trying to find the professors who are in every committee that 'piper' is in (answer should be piper and bill):

I have the following SQL division query but it's wrong and I can't figure out where the problem is (doesn't return bill, just piper):

select b.profname
from committee b
where not exists 

(select commname
from committee a
where profname = 'piper' and not exists 

(select commname
from committee
where a.profname=b.profname ))

Can somebody help me with this one? Thanks,

Answer 1

Your innermost select isn't using anything from itself in its where clause, so it's always finding something for piper. Try

select distinct b.profname from committee b
where not exists (
    select commname from committee a
    where a.profname = 'piper' and not exists  (
        select commname from committee c
        where c.profname=b.profname and c.commname=a.commname
    )
);