Question

Consider the following functional dependencies: Z -> XYD, X -> Y.

Find the minimal cover of the above.

Answer 1

Solution:

Given,

=>Functional dependencies = {Z -> XYZ, X -> Y}

Explanation:

Finding minimal cover:

Step 1:

=>Split the functional dependencies such that there is only single attribute at the right hand side part of every functional depdencies.

=>Functional dependencies = {Z -> X, Z -> Y, Z -> Z, X -> Y}

Step 2:

=>Removing trivial or redundant functional dependencies.

=>Functional dependency Z -> Z is trivial hence removing it.

=>Functionald dependency Z -> Y is redundant because we can derive functional dependency Z -> Y using Z -> X and X -> Y hence removing it also.

=>Functional dependencies = {Z -> X, X -> Y}

Step 3:

=>Finding extraneous attributes.

=>As there is no extraneous attributes in the given functionald dependencies hence this step is not required.

=>Functional dependencies = {Z -> X, X -> Y}

=>Hence minimal cover of given functional dependencies set = {Z -> X, X -> Y}

I have explained each and every part with the help of statements attached to the answer above.