Let $L_1, L_2$ be any two context-free languages and $R$ be any regular language. Then which of the following is/are CORRECT? I. $L_1 \cup L_2$ is context-free. II. $\overline{L_1}$ is context-free. III. $L_1 - R$ is context-free. IV. $L_1 \cap L_2$ is context-free.

Let us examine the closure properties of Context-Free Languages (CFLs):

1. Statement I is TRUE: Context-free languages are closed under union. If $L_1$ and $L_2$ are CFLs, $L_1 \cup L_2$ is context-free.

2. Statement II is FALSE: Context-free languages are not closed under complementation. The complement $\overline{L_1}$ is not necessarily context-free.

3. Statement III is TRUE: CFLs are closed under set difference with regular languages. Since $L_1 - R = L_1 \cap \overline{R}$, and regular languages are closed under complementation, $\overline{R}$ is regular. The intersection of a CFL and a regular language is always a CFL, so $L_1 - R$ is context-free.

4. Statement IV is FALSE: Context-free languages are not closed under intersection. $L_1 \cap L_2$ is not necessarily context-free.

Thus, statements I and III only are correct, corresponding to option (B).