Consider the following languages-L1- 0p 1q 0r - p-q-r- 0 L2- 0p 1q 0r - p-q-r- 0- p- r Which one of the following statements is FALSE-

L_1 is regular so complement of nbsp;L_1 will also be regular. L_2 is context free so complement of nbsp;L_2 will not be regular L_1∩ L_2 is CFL but not reg ...

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Closure properties of CFL Part - 1

Consider the ...

Question

Consider the following languages:
$L_{1} = {0^{p} 1^{q} 0^{r} | p, q, r \geq 0}$
$L_{2} = {0^{p} 1^{q} 0^{r} | p, q, r \geq 0, p \neq r}$
Which one of the following statements is FALSE?

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Solution

$L_{1}$ is regular so complement of $L_{1}$ will also be regular.
$L_{2}$ is context-free so complement of $L_{2}$ will not be regular
$L_{1} \cap L_{2}$ is CFL but not regular.

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Q. Consider the language

L_{1}, L_{2}, L_{3}

as given below:

L_{1} = {0^{p} 1^{q} | p, q \geq 0}

L_{2} = {0^{p} 1^{q} | p, q \geq 0 and p = q}

L_{3} = {0^{p} 1^{q} 0^{r} | p, q, r \geq 0 and p = q = r}

Which of the following statements is NOT true?

Q. Consider the following languages

L_{1}

0^{p} 1^{q} 0^{r} | p, q, r \geq 0

}

L_{2}

0^{p} 1^{q} 0^{r} | p, q, r \geq 0, p \neq r

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Which one of the following statements is FALSE?

Q. Consider the languages L1, L2 and L3 are given below:
L1 = {

0^{p} 1^{q} | p, q ϵ N

},
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0^{p} 1^{q} | p, q ϵ N

and p = q} and
L3 = {

0^{p} 1^{q} 0^{r} | p, q, r ϵ N

and p = q = r}
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Consider the following languages: L1={0p 1q 0r | p,q,r≥0} L2={0p 1q 0r | p,q,r≥0, p≠r} Which one of the following statements is FALSE?

L1 is regular so complement of L1 will also be regular. L2 is context-free so complement of L2 will not be regular L1∩L2 is CFL but not regular.

Consider the following languages:
$L_{1} = {0^{p} 1^{q} 0^{r} | p, q, r \geq 0}$
$L_{2} = {0^{p} 1^{q} 0^{r} | p, q, r \geq 0, p \neq r}$
Which one of the following statements is FALSE?

$L_{1}$ is regular so complement of $L_{1}$ will also be regular.
$L_{2}$ is context-free so complement of $L_{2}$ will not be regular
$L_{1} \cap L_{2}$ is CFL but not regular.