I am getting lost in semantics and need a guide.  I'm writing an app
that keeps track of grades for students in multiple courses.
Depending on the type of course, there will be different categories of
grades ('Lab Assignments','Oral Presentation', 'Programming
Assignments', ...) and there will be different weights for the grades
of different categories.  So let me lay out some tables:

Weights table
   course_id
   category_id
   number
   weight

Categories table
   category_id
   description

Courses
  course_id
  course_name


So it is obvious to me that the Weights table "belongs to" the Courses
and Categories tables.
When I set up the weights that is strait forward to me.  My problem
comes when I start thinking about how to write the model for the
Categories table. According to a book I am reading, "each relationship
with association mapping must be specified in both directions" and
when describing the "other direction" in the relationship between
Categories and Weights or between Categories and Courses I have
exactly 3 options: "Has One", "Has Many" and "Has and Belongs To
Many"...

Which is right for the relationship between Categories and Weights?
and why?
Which is right for the relationship between Categories and Courses?
and why?

Thank you very much for your help!


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