GATE | GATE CS 2010 | Question 65
Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?
(A) L2 – L1 is recursively enumerable.
(B) L1 – L3 is recursively enumerable
(C) L2 ∩ L1 is recursively enumerable
(D) L2 ∪ L1 is recursively enumerable
A) Always True (Recursively enumerable - Recursive ) is Recursively enumerable B) Not always true L1 - L3 = L1 intersection ( Complement L3 ) L1 is recursive , L3 is recursively enumerable but not recursive Recursively enumerable languages are NOT closed under complement. C) and D) Always true Recursively enumerable languages are closed under intersection and union.