Solution

The correct answer is option 3.

Key Points

 L̅REC ∪ LRE  = (Recursive  ∪ Recursively enumerable)=  Recursively enumerable

Recursive languages closed under complement so,  L̅REC is Recursive. Union of recursive and recursively enumerable is recursively enumerable.

L̅CF ∪ LREC    = (not Context-free ∪ Recursive ) =(Recursive ∪ Recursive)= Recursive.

Context-free is not closed for a complement so, L̅CF is Recursive.  The union of recursive and recursive is recursive.

LR ∩ LCF         = (Regular ∩ Context Free ) = Context Free.

The intersection of regular and context-free is Context Free.
∴ Hence the correct answer is A - I, B - II, C - III.

Additional Information