Let $R_1 \left(\underline{A}, B, C\right)$ and $R_2\left(\underline{D}, E \right) $ be two relation schema, where the primary keys are shown underlined, and let C be a foreign key in $R_1$ referring to $R_2$. Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances $r_1$ and $r_2$. Which of the following relational algebra expressions would necessarily produce an empty relation?

$\Pi_D (r_2)  \Pi_C (r_1)$

$\Pi_C (r_1)  \Pi_D (r_2)$

$\Pi_D \left(r_1 \bowtie_{C \neq D}r_2\right)$

$\Pi_C \left(r_1 \bowtie_{C = D}r_2\right)$