question-consider the languages L1 , L2 and L3 as given below

L1={ 0^{p}1^{q}| p,q € N }

L2={0^{p} 1^{q}|p,q € N and p=q }

L3={ 0^{p} 1^{q} 0^{r}| p,q,r € N and p=q=r}. which of the following statements is** not true?**

(a) PDA or DPDA can be used to recognize to L1 and L2

(b) L1 is a regular lang.

(c) all the three lang. are CFL

(d) Turing m/c can be used to recognize all languages

answer-----

L1 - If in a language having no any comparison or linear or having zero memory ( having no stack accept by FA M/C or DPDA M/C) here p,q belongs to natural no. and having no any comparison. therefore language L1 is regular.

L2- If in a language having one comparison or one stack is required ( accept by PDA M/C OR DPDA M/C ).

language will be CFL . In given L2 lang p,q belongs to N and one comparison between p and q i.e p=q. therefore L2 is CFL.

L3 -If in a language having two or more comparison and two or more stacks are required (accepted by NPDA M/C OR LBA M/C). In given L3 language comparison between p, q and r will be p=q,p=r, q=r, p=r ( 4 comparisons) . Therefore L3 language is CSL.

SO, choice(C) is correct a/c to question.