Database Design Redundant Functional Dependencies (FD's)

Question

I have not understood how the following problem must be approached. Any help in learning how to solve this question will be much appreciated!

Consider Relation Schema R = {ABCDEFG} with a set of Functional Depenedencies
F = {GA -> D,   DC -> E,   GF -> A,   CA -> GB,   AF -> D,   F -> G}
Identify any redundant Functional Dependencies.

Answer 1

Consider GA -> D. To check whether it is redundant we need to check whether we can infer D from GA by using dependencies other than GA -> D. However, no other dependency is applicable to GA so GA -> D is not redundant.

Consider AF -> D. If we know AF, then we also know AFG since F -> G. Moreover, since GA -> D we also know D. Hence, we have inferred D from AF without using the dependency AF -> D meaning that AF -> D is redundant.

If your lecture slides also discuss redundant (extraneous) attributes you can check that G is an extraneous attribute in GF -> A since F -> G.