Question

Consider the relation R(A, B, C, D, E), where it is known that the only keys are {A, C, D} and {D, E}:

Give a set of functional dependencies that will make {A, C, D} and {D, E} be the only keys of R. This set should be such that if you delete any FD, then the keys of R will be something other than {A, C, D} and {D, E}.

Answer 1

Candidate Key:

A candidate key is an attribute or set of attributes that uniquely and minimally identify an entity instance in an entity set or record in a table. In a single table, there may be more than one candidate keys.

Primary Key:

The primary key is one of the selected keys from the list of candidate keys to identify the record uniquely.  

Functional Dependency:

It is a relationship between two attributes in which the right-hand side attribute is functionally dependent on the left-hand side attribute.

If the value of attribute Y is determined by the value of X then it is represented as given below:

X → Y

The given relation is:

R(A, B, C, D, E)

The given keys are:

{A,C,D}

{D,E}

As per the given details, the functional dependencies will be as given below:

{A,C,D} -> B

{A,C,D} -> E

{D,E} -> A

{D,E} -> B

{D,E} -> C