13. Given a relation R(A, B, c, D) with the functional dependencies F-(ABC-D, D-
ID: 3709400 • Letter: 1
Question
13. Given a relation R(A, B, c, D) with the functional dependencies F-(ABC-D, D--C], what is the highest normal form the relation is in? a) INF b) 2NF c) 3NF d) BCNF 14. Given a relation R(A, B, C) with primary key AB and functional dependencies {AB-C, C AL suppose we decompose R into two new relations RI (?, A) and R2(B, C). Does this decomposition pass the binary decomposition lossless join test? a)Yes b) No 15. The augmentation rule of inference tells us what? a) ?fA--BC, then it is true that A?B and ??C. b) ABC-AB is true. c) ifA--B, then it is true that AX?BX d) ?fA?B and IX?C, then it is true that AX?C.Explanation / Answer
Answer is as follows:
a) Correct Option is b i.e. 3NF.
Because in the given functional dependencies , there can't exist a transitive dependency that means it follows the 3NF becaause in 3NF if x-> y than x should be a candidate key or y shoulf be prime attribute.
In the given dependecies the genearated candidate key is
{ABC} = {ABCD}
Where ABC -> D , ABC is super/Candidate key
D-> C, C is prime attribute i.e. part of candidate key.
It is not in BCNF because in BCNF if x-> y than x should be primary key, but in given case D is not a candidate key.
b) The correct Option is no.
There will be loss of data due to decomosition because primary key AB is divided into different relations.
c) Correct Option is C
i.e. if A -> B than it is true tht AX -> BX
if there is any query please ask in comments...
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