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.
Ans: D. Let us see each option carefully.
A) Any relation with 2 attributes will be in BCNF. How? Let's assume R(a,b).There can be types of FDs in this relation, 1)a->b ad 2) b->a . If there is no FD, we can assume trivial FDs as ab->a and ab->b.
In all cases, FDs like X->Y, X is key.right. So they all will be BCNF, irrespective of the FD set.So Relation with 2 attributes will be in BCNF, for sure.It is TRUE.
B) If in the relation each key is single attribute, then there is not chance of forming partial FDs for non prime attributes too. Then it will be in 2NF. TRUE statement.
C) Yes it is TRUE. Prime attribute are allowed for transitive dependency.
D) It is FALSE statement.
Please let me know if I am unclear or wrong.