# Recursive Language

 Question 1
Which of the following statements is/are TRUE?
MSQ
 A Every subset of a recursively enumerable language is recursive. B If a language $L$ and its complement $\bar{L}$ are both recursively enumerable, then $L$ must be recursive. C Complement of a context-free language must be recursive. D If $L_1$ and $L_2$ are regular, then $L_1 \cap L_2$must be deterministic context-free.
GATE CSE 2022   Theory of Computation
Question 1 Explanation:
 Question 2
Let < M > denote an encoding of an automaton M. Suppose that $\Sigma =\{0,1\}$. Which of the following languages is/are NOT recursive?
 A $L= \{ \langle M \rangle \mid M \text{ is a DFA such that } L(M)=\emptyset \}$ B $L= \{ \langle M \rangle \mid M \text{ is a DFA such that } L(M)=\Sigma ^ * \}$ C $L= \{ \langle M \rangle \mid M \text{ is a PDA such that } L(M)=\emptyset \}$ D $L= \{ \langle M \rangle \mid M \text{ is a PDA such that } L(M)=\Sigma ^ * \}$
GATE CSE 2021 SET-1   Theory of Computation
Question 2 Explanation:

 Question 3
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
GATE CSE 2018   Theory of Computation
Question 3 Explanation:
 Question 4
If L and P are two recursively enumerable languages then they are not closed under
 A Kleene star $L^{*}$ of L B Intersection $L \cap P$ C Union $L \cup P$ D Set difference
ISRO CSE 2017   Theory of Computation
Question 4 Explanation:
 Question 5
Given the following statements
S1 : Every context-sensitive language L is recursive
S2 : There exists a recursive language that is not context-sensitive
Which statements are true?
 A Only S1 is correct B Only S2 is correct C Both S1 and S2 are not correct D Both S1 and S2 are correct
ISRO CSE 2017   Theory of Computation
Question 5 Explanation:

There are 5 questions to complete.