GATE CS 2024 Set 1 Q12 — Normal Forms

To determine which statements are true for a relation $R$ in First Normal Form (1NF), let us analyze each option based on the definition of 1NF:

• Option A: $R$ can have a multi-attribute key. (TRUE)
  A multi-attribute (composite) candidate key is perfectly allowed in 1NF. In fact, Second Normal Form (2NF) is specifically designed to eliminate partial dependencies, which can only exist when a relation has a multi-attribute candidate key. For example, in $R(\underline{Student\_ID, Course\_ID}, Grade)$, the key is $\{Student\_ID, Course\_ID\}$.
• Option B: $R$ cannot have a foreign key. (FALSE)
  1NF only places constraints on the atomicity of attribute values. It does not restrict the presence of foreign keys, which are essential for establishing relationships between tables.
• Option C: $R$ cannot have a composite attribute. (TRUE)
  By definition, a relation is in 1NF if and only if the domain of every attribute contains only atomic (indivisible) values. This explicitly forbids composite attributes (e.g., an Address attribute split into Street, City, and Zip) and multi-valued attributes.
• Option D: $R$ cannot have more than one candidate key. (FALSE)
  A relation in 1NF can have multiple candidate keys. For example, in $R(\underline{Employee\_ID}, \underline{PAN}, Name)$, both $\{Employee\_ID\}$ and $\{PAN\}$ are valid candidate keys.

Thus, the correct options are A and C.