Anomalies Due to Particular Characteristics in Each,

¶ … anomalies" Due to particular characteristics in each, they may involve errors and cause difficulties in maintaining the consistency of the data as well as requiring unnecessary updates.

To show why this is so, we will take each singly and provide examples:

Insertion Anomalies -- Giving the example of creating a database for employees: inserting a new employee tuple into EM P_DEPT, necessitates that we include in the database either the inclusive attributes of the department that the employee works for or the characteristic NULL if the employee is still between departments. All attribute values of the specific department must be entered correctly so that they are consistent with that department in other tuples of EM P_DEPT. This means constant revision and updating when any slight change occurs in any one of these instances. If even one instance is overlooked, the result is inconsistency.

2. Deletion Anomalies - In other databases, DEPARTMENT tuples are stored separately therefore deletion of one component will not affect others. However here, if we deleted an employee tuple from EMP_DEPT that happened to be the last employee hired by that department, all information concerning that department is lost from the database.

3. Modification Anomalies -- If one changes the value of one of the attributes of a certain department, one has to simultaneously update the tuples of all the employees who work in that department otherwise the database will show inconsistency in that other employee tuples will show up with two differing values.

In other words, each of these characteristics are bothersome and frustrating in that they require constant updating of particulars and may easily mess up the system and provide errors and inconsistency.

"What is meant by the closure of a set of functional dependencies? Illustrate with an example."

The closure is the full set of values that can be determined from a set of known values (e.g. . . A -> B; B -> C) for a given relationship using its functional dependencies. Armstrong's axioms -- such as Reflexivity, Transivity, and Augmentation are used to test the strength of the argument.

An example of a thermo of Functional dependencies is the following:

1. A -> B

2. B -> C

3. AB -> D

We want to provide closure for this set of functional dependencies.