GATE | GATE-CS-2007 | Question 62

Which one of the following statements if FALSE?
(A) Any relation with two attributes is in BCNF
(B) A relation in which every key has only one attribute is in 2NF
(C) A prime attribute can be transitively dependent on a key in a 3 NF relation.
(D) A prime attribute can be transitively dependent on a key in a BCNF relation.


Answer: (D)

Explanation:
If a relational schema is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist.

A relational schema R is in BCNF form if and only if for every one of its dependencies X → Y, at least one of the following conditions hold :
1. X → Y is a trivial functional dependency i.e. Y is a subset of X .
2. X is a super key for schema R

So, we check transitive dependency for only non-prime attributes in case of BCNF.

Thus, the statement ‘A prime attribute can be transitively dependent on a key in a BCNF relation’ is false.

 
Thus, option (D) is the answer.

 
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