Do we keep reflexibility functional dependency in minimal cover

Question

Assume I have to come up the minimal cover of a set of functional dependencies. I have this functional dependency {A,B,C} -> {C}. We would know that {A,B} is redundant and we should remove these two attribute to get the minimal cover. This will leave us with {C} -> {C}, but this is trivial due to reflexibility. Do we still retain {C} -> {C} or remove it as well?

Thanks in advance!

Answer 1

Any dependency of the form:

X → Y

where Y ⊆ X (Y is a subset of X), is called a “trivial dependency”, and is always true by definition. So, it should be removed from the minimal cover. Formally, it is removed in the third step of the algorithm that produces a minimal cover, where redundant dependencies are eliminated.