A relation R is in Third Normal Form (3NF) if it is in 2NF and:
3NF is defined as having no transitive dependencies for non-prime attributes, which is formally expressed as: for every non-trivial X -> Y, X must be a superkey OR Y must be a prime attribute. Thus, both (A) and (B) are valid defining conditions. Therefore, none of the first three statements is correct.
Consider relation R(A, B, C) where A is the candidate key and F = {A -> B, B -> C}. In which highest normal form is relation R?
A is a single-attribute key, so R is in 2NF. However, A -> B and B -> C means non-prime attribute C is transitively dependent on key A via non-prime B. Thus, R violates 3NF, leaving 2NF as its highest normal form. In the revised options, none of (A), (B), or (C) states the required condition, so (E) is correct.
Boyce-Codd Normal Form (BCNF) is a stricter version of which normal form?
BCNF (sometimes referred to as 3.5NF) is a stricter variant of 3NF that eliminates anomalies arising from multiple overlapping candidate keys. The revised options contain two correct statements, so (D) is the appropriate choice.
A relation schema R is in BCNF if for every non-trivial functional dependency X -> Y:
In BCNF, the condition that allows Y to be a prime attribute (present in 3NF) is dropped; the determinant X must strictly be a super key for every non-trivial FD.
Which condition is permitted in 3NF but strictly forbidden in BCNF?
3NF allows an FD X -> Y where X is not a superkey provided Y is a prime attribute. BCNF strictly disallows this exception. The revised options contain two correct statements, so (D) is the appropriate choice.