The set of all recursively enumerable languages is

Let us analyze the properties of the set of all Recursively Enumerable (RE) languages:

• Closure under intersection: If $L_1$ and $L_2$ are recursively enumerable, there exist Turing machines $M_1$ and $M_2$ that recognize them. We can construct a Turing machine that runs $M_1$ and $M_2$ in sequence (or in parallel) on an input $w$, accepting if and only if both accept. Thus, RE languages are closed under intersection (Option B is correct).

• Option A is incorrect: RE languages are not closed under complementation (e.g., the Halting Problem language is RE, but its complement is not RE).

• Option C is incorrect: Recursive languages are a proper subset of recursively enumerable languages, not the reverse ($REC \subset RE$).

• Option D is incorrect: Every RE language is recognized by some Turing machine. Since the description of any Turing machine is a finite binary string, the set of all Turing machines is countably infinite. Therefore, the set of all RE languages is countably infinite, not uncountable.