Let L1L2 be any two context-free languages and R be any regular language- Then which of the following is-are CORRECT-I- L1 - L2 is context-free-II- L-1- is context-free-III- L1-R is context-free-IV- L1 - L2 is context-free-

I. nbsp; L_1 ∪ L_2 is context free = CFL ∪ CFL = CFL So, True II. nbsp; nbsp;L̅_̅1̅ is context free = CFL=CSL but not CFL. So, False III. nbsp;L_1 R is ...

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Closure properties of CFL Part - 2

Let L1L2 be a...

Question

Let $L_{1} L_{2}$ be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT?
I. $L_{1} \cup L_{2}$ is context-free.
II. $_{1}$ is context-free.
III. $L_{1} - R$ is context-free.
IV. $L_{1} \cap L_{2}$ is context-free.

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Solution

I. $L_{1} \cup L_{2}$ is context-free = CFL $\cup$ CFL = CFL So, True
II. $_{1}$ is context-free = $¯ ¯¯¯¯¯¯¯¯¯¯ ¯ C F L = C S L$ but not CFL. So, False
III. $L_{1} - R$ is context-free = CFL $\cap$ $¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ R e g u l a r$ = CFL. So, True
IV. $L_{1} \cap L_{2}$ is context-free = CFL $\cap$ CFL = CSL. So,False

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Similar questions

Q. Let

L_{1}

be a regular language and

L_{2}

be a context-free language. Which of the following languages is/are context-free?

Q. Consider the following types of languages

L_{1} : R e g u l a r, L_{2} : C o n t e x t - f r e e, L_{3} : R e c u r s i v e, L_{4} : R e c u r s i v e l y e n u m e r a b l e .

Which of the following is/are TRUE?
I.

_{3} \cup L_{4}

is recursively enumerable.
II.

_{2} \cup L_{3}

is recursive.
III.

_{1} \cap L_{2}

is context-free.
IV.

L_{1} \cup_{2}

is context-free.

Q. For any two language

L_{1} a n d L_{2}

such that

L_{1}

is context free and

L_{2}

is recursively enumerable but not recursive, which of the following is/are necessarily true?
1.

_{1}

(complement of

L_{1}

) is recursive
2.

_{2}

(complement of

L_{2}

) is recursive
3.

_{1}

is context-free
4.

_{1} \cup L_{2}

is recursively enumerable

Q. Suppose that

L_{1}

is a regular language and

L_{2}

is a context-free language.Which one of the following languages is NOT necessarily context-free?

Q. If

L_{1}

is a context free language and

L_{2}

is a regular language which of the following is are false?

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Let L1L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT? I. L1 ∪ L2 is context-free. II. ¯L1 is context-free. III. L1−R is context-free. IV. L1 ∩ L2 is context-free.

I. L1 ∪ L2 is context-free = CFL ∪ CFL = CFL So, True II. ¯L1 is context-free = ¯¯¯¯¯¯¯¯¯¯¯¯CFL=CSL but not CFL. So, False III. L1−R is context-free = CFL ∩ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯Regular = CFL. So, True IV. L1 ∩ L2 is context-free = CFL ∩ CFL = CSL. So,False

Let $L_{1} L_{2}$ be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT?
I. $L_{1} \cup L_{2}$ is context-free.
II. $_{1}$ is context-free.
III. $L_{1} - R$ is context-free.
IV. $L_{1} \cap L_{2}$ is context-free.