UGC NET CSE | October 2020 | Part 2 | Question: 71

Question

 

Match $\text{List I}$ with $\text{List II}$

$L_R:$ Regular language, $LCF$: Context free language

$L_{REC}:$ Recursive langauge, $L_{RE}$: Recursively enumerable language.

$\begin{array}{llll} & \text{List I} & & \text{List II} \\ (A) & \text{Recursively Enumerable language} & (I) & \overline{L}_{REC} \cup L_{RE} \\ (B) & \text{Recursive language} & (II) & \overline{L}_{CF} \cup L_{REC} \\ (C) & \text{Context Free language} & (III) & L_R^* \cap L_{CF} \end{array}$

Choose the correct answer from the options given below:

• A. $A-II, B-III, C-I$
• B. $A-III, B-I, C-II$
• C. $A-I, B-II, C-III$
• D. $A-II, B-I, C-III$

Answer 1

(A)  Recursively Enumerable will match (I) as complement of REC is always REC hence RE                                                                       too & RE are closed under U

 (B)  Recursive language will match       (II) as complement of CFL is always REC & REC

                                                                     languages  are closed under union

 (C)  Context Free language will match  (III) as intersection of regular and CFL is always CFL

Hence ans is option 3