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Previous Year Question (PYQs)

An organization needs to maintain database having five attributes $A,B,C,D,E$. These attributes are functionally dependent on each other for which functional dependency set $F$ is given as:

$F={A\rightarrow BC,\ D\rightarrow E,\ BC\rightarrow D,\ A\rightarrow D}$

Consider a universal relation $R(A,B,C,D,E)$ with functional dependency set $F$. Also all attributes are simple and take atomic values only.

Identify the redundant functional dependency in $F$.

Given:

$F={A\rightarrow BC,\ D\rightarrow E,\ BC\rightarrow D,\ A\rightarrow D}$





Solution

We need to check which functional dependency can be derived from the other dependencies.

Given:

$A\rightarrow BC$

and

$BC\rightarrow D$

So, by transitivity:

$A\rightarrow BC\rightarrow D$

Therefore,

$A\rightarrow D$

can be derived from $A\rightarrow BC$ and $BC\rightarrow D$.

So, $A\rightarrow D$ is redundant.


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