Which of the following statements is/are TRUE?

Let us analyze each statement:

• (A) False: Every language is a subset of $\Sigma^*$, and $\Sigma^*$ is regular (and hence recursively enumerable). Since there are uncountably many subsets of $\Sigma^*$ but only countably many Turing machines (and thus countably many recursive/RE languages), not every subset of an RE language is recursive (in fact, some are not even RE).

• (B) True: By Post's Theorem, a language $L$ is recursive (decidable) if and only if both $L$ and its complement $\overline{L}$ are recursively enumerable (Turing-recognizable).

• (C) True: Every context-free language (CFL) is recursive. Because the class of recursive languages is closed under complementation, the complement of any CFL is always recursive (even though it may not be context-free).

• (D) True: Regular languages are closed under intersection, so if $L_1$ and $L_2$ are regular, $L_1 \cap L_2$ is regular. Since every regular language is a deterministic context-free language (DCFL), $L_1 \cap L_2$ is deterministic context-free.

Thus, statements B, C, and D are TRUE.