## closure of a set of functional dependencies

Post 1:- A functional dependency is a dependency in nature, not a conceptual dependency because it holds for the data to be logically related.The attributes in a functional dependency are often called the dependent attribute, and the other is called the principal attribute (McMurray et al., 2021). Functional dependencies are usually expressed as mathematical functions in functional analysis and mathematical-statistics texts. We will consider two semantics equivalent if they agree for every instance that satisfies the schema and assign the same set of functional dependencies. For any relation schema R and any models a, a’: R, if the FDs are given according to the first semantics, and a’ according to the second semantics, then the two sets of FDs are equal. Let FDK denote the class of all collections of functional dependencies. We will define a relation schema R as consistent (in FDK) if the location of functional dependencies of any instance in R is constant (in FDK). A standard method for modeling a functional dependency is the foreign key (McMurray et al., 2021). Dependencies are used for machine learning applications. In the context of machine learning, a dependency can represent, for example, a feature dependency, a categorical dependency, a semantic dependency, a lexical dependency, or a grammatical dependency. As examples of feature dependencies, a dependency is often used to express a dependency between a given input text string and a predicted output. In some instances, a result may be represented as a series of one or more feature values (McMurray et al., 2021).

Post 2 :- Closure of a set of functional dependencies is attained from a set of functional dependencies. It is also called a complete set of functional dependencies. When creating a database, we reduce redundancy by collecting a set F of functional dependencies that shows the challenges of the application under development (Charfi et al., 2017). It is necessary to obtain an F which is the largest but the practice is difficult to collect.

Sometimes, it is very easy to make observations of a set of functional dependencies but others are subtle and harder to make observation. There are a set of functional dependencies that can be derived from the easy ones for collection purposes. It is possible to rescue some functional dependencies that have skipped our attention. For those functional dependencies that cannot be retrieved from the easy ones, there is nothing to be done and designing have to continue without them. Since some functional dependencies cannot be obtained from the easy ones, data professionals are hence, not able to create perfect designs.

To find the closure of a set of attributes, it must check if a set of attributes is a Super-key. When determining the function of x, it need to consider looking at the closure of a set of attributes x that can be denoted by X+ (Varga, 2019). when it have a closure problem to compute, it need to have a set of functional dependencies with a set of x for finding the closure. While using abstract examples, we get the database designs. Using the abstract examples, we can calculate a set of dependencies. Given that R(A,B,C,D,E,F). The functional dependencies can be in the form of (AB->C, BC-AD, D->E, CF-.B}. what is {A,B}+?. Starting with (A, B), we have AB-> C to add C to {A, B}+. Lastly {A, B}+ is {A,B,C,D,E}.