GATE CS 2011 Q12 — Normal Forms

To determine which option is INCORRECT, let's analyze each statement based on the properties of the attributes in the relation:

1. Option B: $\text{Registration\_Num}$ can be a primary key
   Since each student has a unique registration number and the table contains exactly one record per registered student, $\text{Registration\_Num}$ uniquely identifies each tuple. Thus, it is a candidate key and can be chosen as the primary key. This statement is correct.
2. Option C: $\text{UID}$ is a candidate key if all students are from the same country
   $\text{UID}$ is unique at the national level. If all students belong to the same country, every student will have a unique $\text{UID}$. Since there is a single record per student, $\text{UID}$ uniquely identifies each record. Thus, it is a candidate key. This statement is correct.
3. Option D: If $S$ is a super key such that $S \cap \text{UID}$ is $\text{NULL}$ then $S \cup \text{UID}$ is also a superkey
   By definition, any superset of a super key is also a super key. Since $S$ is already a super key, adding any attribute(s) to it (including $\text{UID}$) will result in a super key. This statement is correct.
4. Option A: $\text{BankAccount\_Num}$ is a candidate key
   The problem states that students can have joint accounts. If two different students share a joint bank account and both list it as their primary account, the $\text{BankAccount\_Num}$ value will be the same for both students. Since it is not guaranteed to be unique, $\text{BankAccount\_Num}$ cannot be a candidate key. This statement is incorrect.

Therefore, the incorrect option is A.