GATE | GATE CS 2018 | Question 28

The set of all recursively enumerable languages is

(A) closed under complementation.
(B) closed under intersection.
(C) a subset of the set of all recursive languages.
(D) an uncountable set.

Answer: (B)

Explanation: Recursive Enumerable Language are closed under Union, Intersection, Concatenation and Kleene Closure (but not Complementation).
So, we can easily rule out option (A) and option (B) comes to be TRUE.

Recursive Language are subset of REL, but option (C) is saying opposite, so Option (C) is FALSE.
REL are countable, since set of all Turing Machines are countable. So option (D) is also FALSE.

Only Option (B) is CORRECT.

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