MYSQL:SQL query to return a row only if all the rows satisfy a condition

MYSQL:SQL query to return a row only if all the rows satisfy a condition

Consider three tables -
users
<id, type>
1, a
2, b
3, c
types
<type, training>
a, X
a, Y
b, X
c, X
c, Y
c, Z
training_status
<id, training, status>
1, X, F
2, X, S
2, Y, S
3, X, F
3, Y, S
Each user has a type, and types defines the trainings that each user of a
particular type have to complete.
training_status contains status of all the trainings that a user has taken
and its result (S,F). It a user is yet to take a training, there won't be
any row for that training.
I would like to find out all users that have successfully completed all
the trainings that they have to take.
Here's the direction that I am thinking in:
select id from users join types using (type) left join training_status
using (id,type)
where status NOT IN (None, F);
Obviously this is not the right query because even if the user has
completed one of the trainings, we get that row. In the aforementioned
example, I'd like to get id = 2 because he has completed both trainings of
its type.