# How Do Derived Functional Dependencies Impact Key Candidate Identification?

• MHB
• mathmari
In summary, non-trivial dependencies can be derived from F using Armstrong's Axioms and the key candidates for the relational scheme are AB and CD.
mathmari
Gold Member
MHB
Hey!

Given the relational scheme $R = (A, B, C, D)$ with the set of functional dependencies $F =\{AB \rightarrow C, \ BC \rightarrow D, \ CD \rightarrow A, \ AD \rightarrow B\}$.

1. Give all non-trivial dependencies that can be derived from F. Justify your derived dependencies.
2. What are the key candidates?Could you explain to me what we have to do at 1 ? :unsure:

1. Non-trivial dependencies that can be derived from F include:A $\rightarrow$ D, B $\rightarrow$ D, A $\rightarrow$ C, and B $\rightarrow$ C. To justify these dependencies, we can use Armstrong's Axioms. For example, for the dependency A $\rightarrow$ D, we can use the transitivity axiom to derive it since we have AB $\rightarrow$ C and BC $\rightarrow$ D. Since C is a subset of both AB and BC, we can conclude that A $\rightarrow$ D. 2. The key candidates for this relational scheme are AB and CD. These combinations of attributes have all the other attributes in their respective closure sets and therefore form keys.

## 1. What are functional dependencies?

Functional dependencies are relationships between attributes in a database table. They describe how the values of one or more attributes uniquely determine the values of other attributes.

## 2. Why are functional dependencies important in database design?

Functional dependencies help ensure data integrity and reduce data redundancy in a database. By identifying and organizing relationships between attributes, functional dependencies can help improve the efficiency and accuracy of data retrieval and manipulation.

## 3. How are functional dependencies represented?

Functional dependencies are commonly represented using arrow diagrams or mathematical notation. In arrow diagrams, the dependent attribute(s) are connected to the determinant attribute(s) with an arrow. In mathematical notation, functional dependencies are written as A â†’ B, where A is the determinant and B is the dependent attribute.

## 4. What is the difference between a full functional dependency and a partial functional dependency?

A full functional dependency occurs when the values of all attributes in a table uniquely determine the values of another attribute. A partial functional dependency occurs when the values of only some attributes in a table uniquely determine the values of another attribute. Partial functional dependencies can lead to data redundancy and should be avoided in database design.

## 5. How can functional dependencies be used to improve database performance?

Functional dependencies can be used to optimize database performance by reducing the number of attributes that need to be queried or updated. By organizing data based on functional dependencies, queries and updates can be more efficient and accurate, resulting in improved performance.

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