A set of functional dependencies $X$ is minimal if it satisfies the following conditions:
- Every dependency in $X$ has a single attribute on its right-hand side.
- We cannot replace any dependency $A \to B$ in $X$ with dependency $C \to B,$ where $C$ is a proper subset of $A,$ and still have a set of dependencies that is equivalent to $X.$
- We cannot remove any dependency from $X$ and still have a set of dependencies that is equivalent to $X.$
Option C is violating condition $1$ and hence cannot be a minimal cover. (But condition 1 is only in Navathe and not in books like Korth. So, marks are given for both)
In option A, we have $AC \to H$ but since we have $A \to C,$ this implies $A \to H$ and thus violating condition $2.$ So, option A also is not a minimal cover.
In option B, condition $3$ is violated as $A\to C$ cannot be inferred.
Option D is a minimal cover.
Option C,D also gets mark.