If tiny college has some departments that are classified as "research only" and do not offer courses, the course entity of the college database would be the department entity.
a. existence-dependent on
b. independent of
c. optional of
d. mandatory for

c.Optional of

Explanation:

According to my research on different college structures, I can say that based on the information provided within the question the course entity of the college database would be optional of the department entity. This is because the college has many departments but only some offer courses, therefore the courses are dependant on if the department offers them or not (optional).

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you should think about the answers you give and expect the same form your questions.

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.