UGC NET Computer Science December 2019 | Question 146

Question 146

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Comprehension:
Answer question (146-150) based on the problem statement given below:
An organization needs to maintain database having five attributes A, B, C, D, E.
These attributes are functionally dependent on each other for which functionally dependency set F is given as :
F : { A → BC, D → E, BC → D, A → 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.

Minimal cover F' of functional dependency set F is

1. 1. F'= { A → B, A → C, BC → D, D → E }
2. 2. F'= { A → BC, B → D, D → E }
3. 3. F'= { A → B, A → C, A → D, D → E }
4. 4. F'= { A → B, A → C, B → D, C → D, D → E }

Answer : 1. F'= { A → B, A → C, BC → D, D → E }

Explanation Question 146

Steps to find minimal cover:
Step 1: Write all FDs in such a way that the RHS of each FD contain only single attribute.
A → B
A → C
D → E
BC → D
A →D

Step 2: Then for each FD see whether that RHS attribute can be driven by the LHS attribute using any other remaining FDs, if yes then remove that FD otherwise keep it. Here, below dependency A →D
can be derived by usign other dependencies A → BC and BC → D. hence, we remove dependency A → D. So step 1 results in following FDs:
A → B
A → C
D → E
BC → D

Step 3: Now see the FD which is having 2 or more attributes in its LHS.Then find the closure of LHS attributes and then eliminate the attributes from LHS which are common in clsure. Above BC are two attributes in LHS.
B⁺ = {B}
C⁺ = {C}
Since nothing is common in closure so keep both attributes in LHS.
Hence minimal cover is
A → B
A → C
D → E
BC → D

So, option 1 is correct answer

Simple properties/steps of minimal cover:

1. Right Hand Side (RHS) of all FDs should be single attribute.
2. Remove extraneous attributes.
3. Eliminate redundant functional dependencies.

Reference Example : Find minimal cover of set of functional dependencies Exercise

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