Inference Rules for Functional Dependencies

The registrar gave you four rules about the Enrollment table. A colleague asks a fifth question. If I know the course, do I know the department?

That rule is not on the list. Nobody wrote it down. But it is true anyway, and you can prove it without looking at a single row.

Course_ID -> Instructor is on the list. Instructor -> Dept is on the list. Put them end to end and Course_ID -> Dept has to hold.

What derivation means

A set of dependencies carries more dependencies than the ones written in it. The written ones are given. The rest follow by pure logic.