postgresql join confusion - sql

Question

I'm trying to make this statement work. but I can't figure it out.
List the names of the students who never took the course Databases.
I have this:
select distinct s1.name, e1.section_id
from students s1
inner join enrollment e1 on e1.student_id = s1.id
where e1.course_id != 12
but that doesn't remove the student who took that section, so I'm stuck.
Database looks like (I'm soo sorry, I don't know how to insert the database into here)
table students (
id integer primary key,
name varchar(255),
graduation_date date,
major_id integer references departments(id)
);
insert into students (id, name, graduation_date, major_id) values
(1, 'Joe', null, 10);
insert into students (id, name, graduation_date, major_id) values
(2, 'Amy', '2009-04-22', 20);
insert into students (id, name, graduation_date, major_id) values
(3, 'Max', null, 10);
create table courses (
id integer primary key,
title varchar(255),
units integer,
department_id integer references departments(id)
);
insert into courses (id, title, units, department_id) values
(12, 'Databases', 4, 10);
insert into courses (id, title, units, department_id) values
(22, 'Compilers', 4, 10);
insert into courses (id, title, units, department_id) values
(32, 'Calculus 1', 4, 20);
create table sections (
id integer primary key,
course_id integer not null references courses(id),
instructor_id integer references faculty(id),
year integer
);
insert into sections (id, course_id, instructor_id, year) values
(12, 12, 6, 2007);
insert into sections (id, course_id, instructor_id, year) values
(13, 12, 1, 2008);
insert into sections (id, course_id, instructor_id, year) values
(14, 22, 1, 2008);
insert into sections (id, course_id, instructor_id, year) values
(23, 12, 6, 2009);
create table enrollment (
id integer primary key,
student_id integer not null references students(id),
section_id integer not null references sections(id),
grade_id integer references grades(id)
);
insert into enrollment (id, student_id, section_id, grade_id) values
(14, 1, 12, 8);
insert into enrollment (id, student_id, section_id, grade_id) values
(15, 1, 13, 3);
insert into enrollment (id, student_id, section_id, grade_id) values
(16, 1, 14, 5);
insert into enrollment (id, student_id, section_id, grade_id) values
(17, 1, 32, 1);
insert into enrollment (id, student_id, section_id, grade_id) values
(18, 1, 34, 2);
insert into enrollment (id, student_id, section_id, grade_id) values
(19, 1, 53, 13);
insert into enrollment (id, student_id, section_id, grade_id) values
(24, 3, 12, 2);
insert into enrollment (id, student_id, section_id, grade_id) values
(25, 3, 14, 5);
insert into enrollment (id, student_id, section_id, grade_id) values
(26, 3, 32, 1);
insert into enrollment (id, student_id, section_id, grade_id) values
(27, 3, 34, 2);
insert into enrollment (id, student_id, section_id, grade_id) values
(28, 3, 54, 7);
insert into enrollment (id, student_id, section_id, grade_id) values
(34, 2, 43, 3);
insert into enrollment (id, student_id, section_id, grade_id) values

Answer 1

No, don't join everything and then try to clean up with DISTINCT. That's a bad approach. Instead think of what you want to select first. Then write the query step by step.
The "students who never took the course Databases" are
all students except those who took the course Databases
all students who are not in the set of students who took the course Databases
all students for whom not exists a Databases course enrolement
I have highlighted the keywords needed. So you have three options:
Write a query with EXCEPT
Write a query with NOT IN
Write a query with NOT EXISTS
Try these and come back here if you have further problems.
UPDATE: Now that you solved it (and even accepted my answer :-), here are some ways to write the query:
Query with IN clause:
select name
from students
where id not in
(
select student_id
from enrollment
where section_id in
(
select id
from sections
where course_id = (select id from courses where title = 'Databases')
)
);
Query with EXISTS clause:
select name
from students
where not exists
(
select *
from enrollment
where section_id in
(
select id
from sections
where course_id = (select id from courses where title = 'Databases')
)
and student_id = students.id
);
Query with EXCEPT (which is not so good a solution here, because it queries the students table twice, but sometimes EXCEPT is the straight-forward way to a problem). I am using a join on a subquery here instead of WHERE students.id IN (...), just in order to show the technique.
select name
from students
join
(
select id
from students
except
select student_id
from enrollment
where section_id in
(
select id
from sections
where course_id = (select id from courses where title = 'Databases')
)
) found_students on found_students.id = students.id;
Query with COUNT and HAVING, which looks quite compact. It is however a bit more prone to errors. One thing is not to confuse ON and WHERE in outer joins, another is to count the correct column. We must make sure to count a non-nullable field of table sections, so we are sure none of the student's enrollments matched an actual Databases section.
select s.id, s.name
from students s
left join enrollment e on e.student_id = s.id
left join sections s on s.id = e.section_id
and s.course_id = (select id from courses where title = 'Databases')
group by s.id, s.name
having count(s.id) = 0;

Answer 2

I think the queries above over complicate the topic a bit so I added my own.
SELECT s.*
FROM students s
LEFT JOIN (enrollment e
INNER JOIN sections se
ON se.id = e.section_id
INNER JOIN courses c
ON c.id = se.course_id AND c.title = 'Databases')
ON s.id = e.student_id
WHERE
e.id IS NULL