Question

, Odate, Cust#, Total_amount) ORDER- ITEM(O#, I#, Qty_order… # Consider the following relations for an order-processing application database at \(\mathrm{ABC},\) Inc. ORDER (O#, Odate, Cust#, Total_amount) ORDER-ITEM(O#, I#, Qty_ordered, Total_price, Discount\%) Assume that each item has a different discount. The Total_PRICE refers to one item, OOATE is the date on which the order was placed, and the Total_AMOUNT is the amount of the order. If we apply a natural join on the relations ORDER-ITEM and ORDER in this database, what does the resulting relation schema look like? What will be its key? Show the FDs in this resulting relation. Is it in \(2 \mathrm{NF}\) ? Is it in \(3 \mathrm{NF}\) ? Why or why not? (State assumptions, if you make any.)

Short answer

The resultant schema from joining ORDER and ORDER-ITEM relation is ORDER_JOIN (O#, Odate, Cust#, Total_amount, I#, Qty_ordered, Total_price, Discount%). The key of this relation is {O#, I#}. This schema is in both 2nd and 3rd Normal Form.

Step-by-step solution

Apply Natural Join

In a natural join, two relations are combined based on their common attributes. Here, ORDER and ORDER-ITEM share the attribute O# (Order number). So the resulting relation schema after natural join will be: ORDER_JOIN(O#, Odate, Cust#, Total_amount, I#, Qty_ordered, Total_price, Discount%).

Identify Keys

The key of a relation is an attribute or a set of attributes that uniquely identify a record in the relation. In this case, assuming every order can have multiple items, the combination of O# (Order number) and I# (Item number) forms the primary key of the new relation.

Determine Functional Dependencies

{O#, I#} → {Odate, Cust#, Total_amount, Qty_ordered, Total_price, Discount%}. Here, the left side denotes the determinant and the right side represents the dependant. This means for each combination of Order and Item number, the rest of the attributes' values are determined.

Check for 2NF

A relation is in 2NF if it is in 1NF and every non-prime attribute is fully functionally dependent on the primary key. In our case, every non-prime attribute (all attributes except O# and I#) is fully functionally dependent on the primary key {O#, I#}. Thus, the relation is in 2NF.

Check for 3NF

A relation is in 3NF if it is in 2NF and there is no transitive dependency for non-prime attributes. Here, none of the non-prime attributes depend on other non-prime attributes. Hence, the relation is also in 3NF.

Key concepts

Functional Dependencies

Understanding functional dependencies is essential in database design because they help determine how well a database schema is normalized, which in turn affects the efficiency and integrity of the database.

A functional dependency (FD) occurs when one attribute in a relation uniquely determines another attribute; this is a notion of dependency between the attributes of a database. For example, in a database of student records, the student ID might functionally determine the student's name and other personal details – no two students share the same ID, and for each ID, there is a specific set of details.

In the provided exercise where we have the ORDER and ORDER-ITEM relations, we look at the functional dependency in the combined relation after a natural join. The FDs here signify that given a unique pair of O# (Order number) and I# (Item number), one can determine all the other attributes like Odate, Cust#, Total_amount, Qty_ordered, Total_price, and Discount%. This forms the basis of understanding how we can query our data and also plays a crucial role in the normalization process.

Database Normalization

The term database normalization refers to the process of structuring a relational database to reduce data redundancy and improve data integrity. It involves decomposing tables and establishing relationships through keys—primary and foreign. Normalization is typically done in several stages, each with specific requirements, known as 'normal forms'.

The first normal form (1NF) requires that the table has no repeating groups of data. Second Normal Form (2NF) builds upon 1NF by ensuring that all non-key attributes are fully dependent on the primary key alone. Third Normal Form (3NF) further refines the structure by ensuring that all non-key attributes are only dependent on the primary key and not on other non-key attributes.

In the context of the ORDER and ORDER-ITEM relations, after applying a natural join, we assess whether the new relation is in 2NF and 3NF. Since every non-prime attribute is fully functionally dependent on the combined primary key and there are no transitive dependencies, the resulting relation achieves both 2NF and 3NF, thus adhering to principles of sound database normalization.

Relation Schema

The term relation schema defines the structure of a relation in a relational database, consisting of a list of attributes and their corresponding data types. Think of it as the blueprint for a table, detailing what kind of information the table stores.

A schema may also include constraints that must be met by the data, like primary keys and unique keys that preserve the uniqueness of records. Referring to our exercise, the schema of the joined relation is ORDER_JOIN(O#, Odate, Cust#, Total_amount, I#, Qty_ordered, Total_price, Discount%), with O# and I# forming the primary key. This schema gives an overview of how data is organized after the natural join operation, laying the groundwork for queries, updates, and maintenance practices within a database system.

It's important to have a well-defined relation schema as it impacts the maintainability, scalability, and efficiency of data retrieval and manipulation. By thoroughly understanding a relation schema, developers and database administrators can guarantee the consistency and validity of data throughout the lifecycle of a database application.