Normalization

Question

Q) Consider the relation R(A,B,C,D) with dependencies AB → C, ABC → D and AC ->> B. Which of the following
statement is true
A. R is not in 3NF
B. R is in 3NF but not in BCNF
C. R is in BCNF but not in 4NF
D. R is in 4NF
For 4nf checking we just simply say there shouldnt be multivalued dependencies but given explaination by nptel is the MVD has a
non-superkey on the left, so it violates 4NF.Plz help

Comments

4th nf   A Table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies X  Y, X is a superkey—that is, X is either a candidate key or a superset thereof.^[1]  

^{but if a table has trivial MVD then it is in 4NF}

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@Sanjay, so you mean AC->>B is in 4NF  since AC is candidate key?

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no the given table is not in 4nf

here AC-->>B is non trivial MVD so  AC must be superkey which is not here

here key is AB  so option C is right

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@Sanjay. Thanks. I had overlooked AC->>B as AC->B and hence thought AC as candidate key.