UGC-NET | UGC-NET CS 2017 Nov – III | Question 9

If every non-key attribute is functionally dependent on the primary key, then the relation is in __________ .
(A) First normal form
(B) Second normal form
(C) Third normal form
(D) Fourth normal form


Answer: (B)

Explanation: Conditions for various normal forms:

1. 1 NF – A relation R is in first normal form (1NF) if and only if all underlying domains contain atomic values only.
2. 2 NF – A relation R is in second normal form (2NF) if and only if it is in 1NF and every non-key attribute is fully dependent on the primary key.
3. 3 NF – A relation R is in third normal form (3NF) if and only if it is in 2NF and every non-key attribute is non-transitively dependent on the primary key.
4. BCNF – A relation R is in Boyce-Codd normal form (BCNF) if and only if every determinant is a candidate key.

Example:
Relation R(XYZ) with functional dependencies {X -> Y, Y -> Z, X -> Z}.
Notice here Y -> Z, in question it is not mention that non prime attribute is only dependent on primary key so this FD is perfectly valid.
This relation is in 2NF but not in 3NF because of every non-key attribute is transitively dependent on the primary key. Here {X} will be candidate key.

So, option (B) is correct.

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