GATE CS 2014 Set 3 Q.32 (CS Q.22): Functional Dependencies and Normalization

A prime attribute of a relation scheme $R$ is an attribute that appears

in all candidate keys of $R$ .

in some candidate key of $R$ .

in a foreign key of $R$ .

only in the primary key of $R$ .

Official answer and solution

Solution

Recall the formal relational database definitions of candidate keys and prime versus non-prime attributes.

In relational database schema design:
- A superkey is a set of attributes that uniquely identifies each tuple in a relation.
- A candidate key is a minimal superkey (no proper subset is a superkey).
Prime Attribute:
An attribute of a relation schema $R$ is defined as a prime attribute if it is a member of at least one (some) candidate key of $R$ .
Non-prime Attribute:
An attribute is non-prime if it does not belong to any candidate key of $R$ .
Thus, a prime attribute does not need to appear in all candidate keys (which would be the intersection of candidate keys), nor is it restricted only to the primary key. It suffices to appear in some candidate key.

Therefore, option B is correct.

Final answer

Common trap

Confusing 'some candidate key' with 'all candidate keys' or thinking prime attributes belong only to the primary key.

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