Final answer:
The statement about a relation schema R being in 3NF if it's in 2NF and no non-prime attribute in R is transitively dependent on the primary key is TRUE. 3NF extends the requirement of 2NF to eliminate transitive dependencies, thus reducing database redundancies and update anomalies.
Step-by-step explanation:
The statement, "A relation schema R is in 3NF (Third Normal Form) if it is in 2NF (Second Normal Form) and no non-prime attribute in R is transitively dependent on the primary key," is TRUE.
For a relation schema to be in 3NF, it must first satisfy the conditions for 2NF, which primarily deals with eliminating the partial dependency of any non-prime attribute on a composite primary key. In 3NF, this requirement is extended to eliminate transitive dependencies, which occur when a non-prime attribute depends on another non-prime attribute that, in turn, directly depends on the primary key. Essentially, in 3NF, every non-prime attribute must be directly dependent on the primary key, rather than indirectly through another non-prime attribute.
By ensuring that a schema is in 3NF, we can reduce redundancy and eliminate certain types of update anomalies, making the database more efficient and reliable. Redundancies and update anomalies are often a problem in databases that aren’t adequately normalized.