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Given: The Relation R(A,B,C,D,E) having (A,B) as Primary key. The set of functional dependencies: (A,C)-->D , (B,D)-->E. I want to Know whether the functional dependencies Given above are Partial FD's or Not?

No, None of $AC \rightarrow D$ and $BD \rightarrow E$  is a Partial dependency.

Partial Dependency :
If a non-prime attribute of the relation is getting derived by only a part of the composite candidate key then such dependency is defined as partial dependency.

Since, $AB$ is the Candidate key here, So, To have Partial dependency in this Relation $A$ only Or $B$ only should have derived any of $C,D,E$. Which is Not the case here.

The Given FD's are Transitive Dependencies :

Transitive Dependency

In Simple words, If a non-prime attribute of the relation is getting derived Transitively by Candidate key(s). So, A Partial Dependency is Also a Transitive dependency. In some sense a partial dependency is a special case of a transitive dependency.

If a non-prime attribute of the relation is getting derived by either another non-prime attribute or by the combination of part of the candidate key along with a non-prime attribute or by a Part of Candidate key then such dependency would be defined as transitive dependency.

Here, in the given relation, the combination of part of the candidate key along with a non-prime attribute is deriving Non-key attribute.

$AC \rightarrow D$ ...Where $A$ is Part of Candidate key and $C,D$ are Non-key attributes.

and $BD \rightarrow E$... Where $B$ is Part of Candidate key and $D,E$ are Non-key attributes.

NOTE that In some sense a partial dependency is a special case of a transitive dependency. On the other hand there are transitive dependencies that are not caused by partial dependencies.

prime attributes:-

which attributes are part of atleast one candidate key.

non-prime attributes :-

which attributes are not part of atleast one candidate key.

prime attribute + non-prime attribute = non-key.

key+prime attribute = key

key+non-prime attribute = key

non-prime attribute + non-prime attribute = non-key

prime attribute + prime attribute = may form the key or part of any candidate key or not pat of any key

According to your question, AB is Primary Key ===> A and B are prime Attributes and C and D are non-prime attributes

∴ AC ==> prime attribute + non-prime attribute = non-key

AC -> D ===> non-key -> non-key ===> Transitive Dependency

∴ BD ==> prime attribute + non-prime attribute = non-key

BD -> E ===> non-key -> non-key ===> Transitive Dependency

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