GATE CS 2021 Set 2 Q6 — Integrity Constraints

To determine the correctness of the statements, let us analyze them individually:

• Statement $S1$: "A relation scheme can have at most one foreign key."
  Analysis: This statement is false. A relation can have multiple foreign keys referencing different relations (or even the same relation).
  Example: Consider an Enrollment relation:
  $$\text{Enrollment}(\underline{\text{student\_id}}, \underline{\text{course\_id}}, \text{grade})$$
  Here, $\text{student\_id}$ is a foreign key referencing the $\text{Student}$ relation, and $\text{course\_id}$ is another foreign key referencing the $\text{Course}$ relation.


• Statement $S2$: "A foreign key in a relation scheme $R$ cannot be used to refer to tuples of $R$."
  Analysis: This statement is false. A relation can contain a self-referencing (recursive) foreign key that references its own primary key.
  Example: Consider an Employee relation:
  $$\text{Employee}(\underline{\text{emp\_id}}, \text{name}, \text{manager\_id})$$
  Here, $\text{manager\_id}$ is a foreign key that references $\text{emp\_id}$ within the same $\text{Employee}$ relation, representing the hierarchical relationship where a manager is also an employee.

Since both statements $S1$ and $S2$ are false, the correct choice is D.