The requirement for a relation schema (r) to be in 2NF (Second Normal Form) is that every non-prime attribute (a) must be fully functionally dependent on any candidate key of r.
To understand this requirement, let's first consider the general definition of 2NF. A relation is in 2NF if it is in 1NF and there are no partial dependencies. In other words, every non-key attribute must be fully functionally dependent on the entire candidate key, not just part of it.
In the context of the requirement mentioned, a non-prime attribute (a) refers to an attribute that is not part of any candidate key. It is an attribute that is not part of the primary key or any unique key.
For a relation schema (r) to be in 2NF, every non-prime attribute (a) should be fully functionally dependent on any candidate key of r. This means that the value of attribute (a) must be determined by the entire candidate key, and not by a subset of the key attributes.
By ensuring that every non-prime attribute is fully functionally dependent on the candidate key, we eliminate any partial dependencies and ensure that the relation schema satisfies the requirements of 2NF. This helps in minimizing redundancy and improving data integrity in the database design.