Modeling #10 - Questions and Answers

Question 1 List the various data abstraction concepts and the corresponding modeling concepts in the EER model. Answer Here is a list of data abstraction concepts and their variants in the EER model: Classification and instantiation - The EER variant of classification is represented by classifying entities into entity types based on their attributes and relationships. Relationship instances become relationship types. For the need of further classification, we introduce superclass/subclass concepts and sometimes even categories. In the EER model, there is no handling of class exceptions and no showing of examples (instances). Identification - EER model implements identification by sticking to the rule of name uniqueness. Every entity type, relationship type, attribute, subclass, superclass, and category has to have a unique name that no other object in a database has. Specialization and Generalization - The concept of specialization and generalization in the EER model is represented by subclasses. They are more specific objects than their respective superclasses and are related to them by IS-A-SUBCLASS-OF (or shortly IS-A) relationship. Aggregation and Association - EER schema uses aggregation abstraction in the form of creating new composite objects. We can aggregate attributes to create a composite attribute, entity type, or even a relationship type if there's a need to. Association in EER modeling is simply a relationship type between two or more independent entity types. Question 2 When does data modeling use the idea of a weak entity? Give definitions for the terms partial key, weak entity type, identifying relationship type, and owner entity type. Answer When specifying a new entity type that is similar to one we already have, the concept of weak entity types is used in data modeling, but we want this new entity type to have specific attributes and to be able to participate in specific relationships. If the newly created entity type lacks important attributes, it is called a weak entity type and it needs to be related to a strong entity type (directly or indirectly) that has key attributes of its own. Owner (or identifying) entity type is a title for entity types that identifies weak entity types related to it. Weak entity types include one of their attributes when combining with the owner entity type. A weak entity type is one that lacks essential properties of its own. Identifying relationship type is a title for relationship type that relates one weak entity type to one owner entity type. In this relationship type, weak entity has a total participation constraint, meaning it cannot exist without its owner entity type that identifies it. Partial key (or discriminator) is an attribute or set of attributes of a weak entity type that distinguishes weak entities related to the same owner entity type. Question 3 Quadrant in which the graph f⁻¹ lie Given information: The graph of f lies entirely in quadrant 1 and 2. Answer Concept used: The graph of the inverse function f⁻¹(x) is a mirror image about the line y = x. Calculation: The graph of quadrant 1 will make its image in quadrant 1 if a mirror is taken about the line y = x. The graph of quadrant 2 will make its image in quadrant 4 if a mirror is taken about the line y = x Therefore, the function f⁻¹ lies in quadrants 1 and 4 if the graph of f lies entirely in quadrant 1 and 2. Conclusion: The function f⁻¹ lies in quadrants 1 and 4 if the graph of f lies entirely in quadrants 1 and 2. Question 4 a) Domain and range of f b) The table for f⁻¹(x) and the domain and range. Given: x | 1 | 10 | 100 | f(x) | 0 | 1 | 2 | Answer Formula used: For the table of inverse functions, the values of x and f(x) are interchangeable. Calculations: 1) x | 1 | 10 | 100 | f(x) | 0 | 1 | 2 | Here the domain of f = {1, 10, 100} The range of f = {0, 1, 2} 2) By switching the rows of x and f, we can obtain the table for the inverse. We get x | 0 | 1 | 2 | f⁻¹(x) | 1 | 10 | 100 | The domain for f⁻¹(x) = {0, 1, 2} The range for f⁻¹(x) = {1, 10, 100} Conclusion: Here the domain of f = {1, 10, 100}. The range of f = {0, 1, 2} x | 0 | 1 | 2 | f⁻¹(x) | 1 | 10 | 100 | The domain for f⁻¹(x) = {0, 1, 2} The range for f⁻¹(x) = {1, 10, 100}