Suppose $R_1(A, B)$ and $R_2(\underline{C}, D)$ are two relation schemas. Let $r_1$ and $r_2$ be the corresponding relation instances. B is a foreign key that refers to C in $R_2$. If data in $r_1$ and $r_2$ satisfy referential integrity constraints, which of the following is ALWAYS TRUE?

Since $B$ is a foreign key in $R_1$ referencing the primary key $C$ in $R_2$, by definition of referential integrity:

• Every non-null value appearing in attribute $B$ of instance $r_1$ must exist in attribute $C$ of instance $r_2$.

• In set-theoretic terms, the projection of $r_1$ on $B$ must be a subset of the projection of $r_2$ on $C$:

  $$\Pi_B(r_1) \subseteq \Pi_C(r_2)$$

• Therefore, the set difference $\Pi_B(r_1) - \Pi_C(r_2)$ is empty:

  $$\Pi_B(r_1) - \Pi_C(r_2) = \varnothing$$

Hence, (A) is ALWAYS TRUE.