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) A
(B) B
(C) C
(D) D


Answer: (B)

Explanation:

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. 


Quiz of this Question



My Personal Notes arrow_drop_up

Recommended Posts:



0 Average Difficulty : 0/5.0
No votes yet.






User Actions