Find minimal cover of set of functional dependencies example, Solved exercise  how to find minimal cover of F? Easy steps to find minimal cover of FDs, What is minimal cover?
Question:
5. Find the minimal cover of the set of functional dependencies given; {A → BC, B → C, AB → D}
Solution:
Minimal cover:
Definition 1:
A minimal cover
of a set of FDs F is a minimal set of functional dependencies F_{min}
that is equivalent to F. There can be many such minimal covers for a set of functional
dependencies F.
Definition 2:
A set of FDs F is
minimum if F has as few FDs as any equivalent set of FDs.

Simple
properties/steps of minimal cover:
1. Right Hand Side (RHS) of all FDs
should be single attribute.
2. Remove extraneous attributes. [What is extraneous attribute? Refer here].
3. Eliminate redundant functional
dependencies.
Let us apply these properties to F = {A
→ BC, B → C, AB → D}
1. Right
Hand Side (RHS) of all FDs should be single attribute. So we write F as
F1, as follows;
F1 = {A → B, A → C, B → C, AB → D}
2. Remove
extraneous attributes.
Extraneous attribute is a redundant
attribute on the LHS of the functional dependency. In the set of FDs, on AB → D
has more than one attribute in the LHS. Hence, we check one of A and B is
extraneous or not.
First we check whether A is extraneous or not. To do that, we need to find the
closure of the remaining attribute B with respect to F1.
B^{+} = BC.
This does not include D, so A is not
extraneous.
Now we check whether B is extraneous or not. To do that, we need to find the
closure of the remaining attribute A with respect to F1.
A^{+} = ABCD.
This includes D, so B is extraneous,
ie., we can identify D without B on the LHS.
Now, we can write the new set of FDs,
F2 as follows;
F2 = {A → B, A → C, B → C, A → D}
3. Eliminate
redundant functional dependency.
If A → B, and B → C, then A → C is
true (according to transitive rule). Hence, the FD A → C is redundant. We can
eliminate this and we get final set of FDs F3 as follows;
F3 = {A → B, B → C, A → D}
The set of FDs F3 is the minimal cover of F.
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Similar topics
How to find closure of set of functional dependencies?
How to find closure of attributes?
How to find canonical cover for a set of functional dependencies?
How to find extraneous attribute?
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