Consider the following types of languages: $L_1$ : Regular, $L_2$ : Context-free, $L_3$ : Recursive, $L_4$ : Recursively enumerable. Which of the following is/are TRUE? I. $\overline{L_3} \cup L_4$ is recursively enumerable II. $\overline{L_2} \cup L_3$ is recursive III. $L_1^* \cap L_2$ is context-free IV. $L_1 \cup \overline{L_2}$ is context-free

Let us analyze each statement based on closure properties:

1. Statement I: $L_3$ is a recursive language. Recursive languages are closed under complementation, so $\overline{L_3}$ is recursive. Since every recursive language is also recursively enumerable (RE), $\overline{L_3}$ is RE. Recursively enumerable languages are closed under union, so $\overline{L_3} \cup L_4$ is recursively enumerable. Hence, Statement I is TRUE.

2. Statement II: $L_2$ is a context-free language (CFL). Since every CFL is recursive, $L_2$ is recursive. As recursive languages are closed under complementation, $\overline{L_2}$ is recursive. Since recursive languages are closed under union, $\overline{L_2} \cup L_3$ is recursive. Hence, Statement II is TRUE.

3. Statement III: $L_1$ is regular, so by Kleene closure, $L_1^*$ is also regular. The intersection of a context-free language and a regular language is always context-free. Therefore, $L_1^* \cap L_2$ is context-free. Hence, Statement III is TRUE.

4. Statement IV: Context-free languages are not closed under complementation, so $\overline{L_2}$ may not be context-free (it is recursive, but not necessarily context-free). The union of a regular language and $\overline{L_2}$ is not necessarily context-free. Hence, Statement IV is FALSE.

Therefore, statements I, II, and III are TRUE, which corresponds to option (D).