UGC NET CSE | November 2017 | Part 3 | Question: 9

Question

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

Comments

Fully functionally dependent or partially functionally dependent ?

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yes , it  should be in 2NF.

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but fully or partially?

Answer 1

Answer - C Third Normal Form.

Why it is not in 2NF:

Let's take simple example:

R: {X→Y,  Y→Z,  X→Z}

In above relation,  in FD Y→Z, Z is clearly Non key attribute and It is NOT dependent on Primary key Because Primary key is X.

Y→Z is not valid functional dependency for the given statement "If every non-key attribute functionally dependent on the primary key". 

We can't take wrong example and prove our answer. 

 3NF Wikipedia definition : "no non-prime attribute depends on other non-prime attributes. All the non-prime attributes must depend only on the candidate keys."  This definition is same as "If every non-key attribute (All the non prime attributes) functionally dependent on the primary key(candidate keys)"

Non prime attribute and Non key attributes are same : http://www.exploredatabase.com/2017/07/define-non-prime-attribute-non-key-attribute-in-dbms.html

 

Answer 2

The functional dependency of X on Y represented by X->Y . 

Now, as per the question every non key attribute is functionally dependent on primary key . So assume X is non key and A is prime attribute then relation looks like : X→ A

This is clearly states FD is in 3NF as Non_Prime → Prime 

So answer will be (C) 3NF

Answer 3

ANSWER-3NF

IT IS IN 3NF BECAUSE ( THE CONDITION FOR 3NF IS THAT LEFT SIDE OF FUNCTIONAL DEPENDENCY SHOULD BE PRIMARY KEY OR RIGHT SIDE SHOULD BE PRIME ATTRIBUTE)

Answer 4

Answer will b 2NF since nothing is mentioned about the non-trivial dependency