To understand why eliminating transitive dependency is important in this case and how it prevents redundancy and anomalies, let's first define what transitive dependency and the related anomalies are.
Transitive Dependency:
A transitive dependency occurs when one attribute indirectly depends on another attribute via a third attribute. In this case, the loan schema has the following functional dependencies:
custname -> loanno (customer name determines loan number).loanno -> amount (loan number determines loan amount).
Thus, we have a transitive dependency: custname -> loanno -> amount. In other words, custname indirectly determines amount via loanno.
This means that the amount column in the original schema depends transitively on custname, and it leads to redundancies and anomalies.
Redundancy and Anomalies:
To illustrate how redundancy and anomalies occur in the original schema, let's consider some example data:
custname | branch | loanno | amount |
|---|
Alice | Branch1 | 101 | 5000 |
Bob | Branch2 | 102 | 3000 |
Alice | Branch1 | 101 | 5000 |
Charlie | Branch3 | 103 | 8000 |
Redundancy:
In the above table, notice how the loan number (loanno) and amount for Alice are repeated twice. This happens because Alice has the same loan number 101, and that loan is associated with a fixed amount of 5000. So, every time Alice's data is inserted into the table, the loan amount 5000 is repeated.
Redundant data leads to unnecessary storage consumption and can increase the cost of managing the database.
Update Anomaly:
Suppose Alice's loan amount changes from 5000 to 5500. You would have to update the loan amount in every row where Alice's loan appears. If you miss updating even one row, the data will be inconsistent (some rows will show 5000, and others will show 5500).
Deletion Anomaly:
If you remove Alice's loan information entirely (by deleting the row), you'll also lose her loan number and amount details. This could be a problem if loan numbers and amounts are needed independently of customer names (for example, for financial audits or reporting).
Insertion Anomaly:
If you want to insert a new loan record for a customer without an associated loan number yet, you can't do it. The schema forces you to have a loan number and an amount, which may not be available at the time of insertion.
Eliminating the Transitive Dependency:
By decomposing the table into two tables (loan1 and loan2), we eliminate the transitive dependency and remove the above anomalies. Here’s the decomposed schema:
loan1(loanno, amount): This table captures the direct relationship between loan number and loan amount.
| loanno | amount |
|---|
| 101 | 5000 |
| 102 | 3000 |
| 103 | 8000 |
loan2(cname, branchname, loanno): This table captures the relationship between the customer and the loan number.
| cname | branchname | loanno |
|---|
| Alice | Branch1 | 101 |
| Bob | Branch2 | 102 |
| Charlie | Branch3 | 103 |
How this fixes the anomalies:
Redundancy: The loan amount is now stored only once in the loan1 table. So, even if multiple customers are associated with the same loan, the amount won’t be duplicated.
Update Anomaly: If Alice’s loan amount changes from 5000 to 5500, you only need to update the loan1 table once (at loan number 101). This ensures data consistency and avoids the risk of partial updates.
Deletion Anomaly: Deleting Alice from loan2 (customer data) won't remove loan details from loan1. Thus, the loan details are preserved even if no customers are currently associated with the loan.
Insertion Anomaly: You can insert a new customer record in loan2 even if their loan amount is not yet known. As long as the loan number is not required at the moment, you can insert partial data.
Summary:
By decomposing the schema to eliminate the transitive dependency, we:
- Reduce redundancy
- Prevent update, deletion, and insertion anomalies
- Improve data consistency and maintainability
This normalization makes the database more efficient and easier to manage.
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