I have a three level database with the following structure (simplified to only show the primary keys):

Table A: a_id
Table B: a_id, b_id
Table C: a_id, b_id, c_id

So possible values for table C would be something like this:

a_id  b_id  c_id
   1     1     1
   1     1     2
   1     1     3
   1     2     1
   1     2     2
   2     1     1
   2     2     1
   2     2     2
...

I am now unsure, how foreign keys should be set; or if they should be set for the primary keys at all. My idea was to have a foreign key on table B B.a_id -> A.a_id, and two foreign key on C C.a_id -> A.a_id and ( C.a_id, C.b_id ) -> ( B.a_id, B.b_id ).

Is that the way I should set up the foreign keys? Is the foreign key from C->A necessary? Or do I even need foreign keys at all given that all those columns are part of the primary keys?

Thanks.