Which of the following statements is/are TRUE?

A.

Every subset of a recursively enumerable language is recursive. 

B.

If a language L and its complement L are both recursively enumerable, then L must be recursive.  

C.

Complement of a context-free language must be recursive.

D.

If L1 and L2 are regular, then L1∩L2 must be deterministic context-free.

Solution:

Option A: False, There exists a set of languages that is Recursively Enumerable but not Recursive, this set is a subset of Recursively Enumerable but is Not Recursive.

Option B: True, If a language L and its complement L are both Recursively Enumerable, then both languages are Recursive. 

Option C: True, All context-free languages are Recursive and Recursive languages are closed under complementation.

Option D: True, Regular languages are closed under intersection and every Regular language is DCFL.