Consider a relation R with five attributes ABCDE. You are given the following dependencies: A à...

Consider a relation R with five attributes ABCDE. You are given the following dependencies: A à B, BC à E, and ED à A.

(1) List all candidate keys for R. Please show your steps. (4 points)

(2) Is R in 3NF? Please explain your answer. (3 Points)

(3) Is R in BCNF? Please explain your answer. (3 Points)

Solutions

Expert Solution

Solution:-

Functional dependencies:
A -> B , BC -> E , ED -> A

1) Since attributes C , D cannot be derived from any of the functional dependencies. So there are definitely present in the Candidate key.
Since, Closure of CD = CD. So now trying possible combinations of CD.
Closure of ACD = ABCDE
Closure of BCD = ABCDE
Closure of ECD = ABCDE

Therefore, Candidate Keys = { ACD , BCD , ECD }.

2) For a relation to be in 3NF it is mandatory that in every non trivial functional dependency Left hand side attribute must be a super key of relation OR Right hand side attribute must be prime attribute of relation.

Prime attributes = { A , B , C , D , E }

Right hand side attribute of each functional dependency: { B , E , A } are Prime attributes.

Therefore, Relation is in 3NF.

3) For a relation to be in BCNF it is mandatory that in every non trivial functional dependency Left hand side attribute must be a super key of relation.

Left hand side attribute of each functional dependency: { A , BC , ED } are not the Super Keys of the Relation.

Therefore, Relation is not in BCNF.

venereology answered 1 year ago

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