Full Answer Section

1. Deletion Anomaly: This happens when deleting one piece of data results in the accidental loss of other related data. For example, if a customer table is not normalized, deleting a customer might also delete their order history.
2. Update Anomaly: This arises when updating data in one place requires updating it in multiple places, leading to inconsistencies. For instance, if a customer’s address is stored in multiple tables, updating it in one place might not update it in all locations.

Closure of a Set of Functional Dependencies

A set of functional dependencies, F, is said to be closed if it contains all the functional dependencies that logically follow from F. In other words, it is closed under implication.

Example:

Consider a relation R(A, B, C) with the following functional dependencies:

• A -> B
• B -> C

The closure of F, denoted as F+, would include:

• A -> B
• B -> C
• A -> C (derived from the transitive rule)

Closure is essential in database design as it helps identify redundant data and potential anomalies. By understanding the closure of functional dependencies, database designers can create efficient and reliable database schemas.

References:

1. Elmasri, R., & Navathe, S. B. (2011). Fundamentals of Database Systems. Addison-Wesley.
2. Silberschatz, A., Korth, H. F., & Sudarshan, S. (2010). Database System Concepts. McGraw-Hill Education.