Help to simplify sample query

Hi guys, i have a new question about how to simplify a query. I have
the tables area_course(cd_area,cd_course) and
teacher_course(cd_teacher,cd_course) and a set of pairs of values
{(1,2),(98,45),(11,0),...}.

Now, i must to select the areas which courses appears in
teacher_course and match with the set of pairs. Something like :

select cd_area from area a1 where
exists (select * from teacher_course c2 where c2.cd_course =
a1.cd_course and c2.cd_teacher = 1 and c2.cd_course = 2) and
exists (select * from teacher_course c2 where c2.cd_course =
a1.cd_course and c2.cd_teacher = 98 and c2.cd_course = 45) and
exists (select * from teacher_course c2 where c2.cd_course =
a1.cd_course and c2.cd_teacher = 11 and c2.cd_course = 0) and
....

This is just a sample. The whole query is giant and its use other
tables/columns. Is there a best way to write this query ?

I don't think this is possible, but: Is there a efficient way to
compare if the result of a query is a superset of the result of another ?

I would appreciate any ideas/suggestions. Thanks !!!