GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 42

Answer 1

Option A:

$L_2$ is CFL, and $L_1 \cap L_2 = \{ a^k b^{2k} c^{2k} | k \geq 0 \}$ is Not CFL.

Option C:
$$
\text {results in } L_1 \cap L_2=\left\{a^n b^n c^n \mid n \geq 0\right\}
$$
Which is Not CFL.

Option B:

The result will be $\{ \epsilon, abc \}$ which is a finite language, so, CFL.

Option D: Language $L_2$ itself is not CFL & the question asks for a CFL.

Comments

Sir, in option A, is that language CFL ? If not, then A can’t be the answer na ? And what is approach for option D ?

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if L2 is D then language is like this AFTER L1 ^ L2 = {E,  abbcc, aabbbbcccc, …….}
now use PDA like start with ‘a’ u can Skip ‘a’ and now push every ‘b’ in stack and When c comes then pop ‘b’ from stack finally stack became empty and string is accepted

so that means L1^L2 is CFL

please correct me if I’m wrong anywhere:D

yes my bad option D itself is not CFL so that means we are not consider them in our answer 

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@ak_dev In the question, it is mentioned that we have to select L2 as a CFL but option D language is not itself CFL. It is CSL. Therefore, we can’t select it as L2.