Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is true?a)I...
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Which of the following statements is true?
- a)If a language is context free it can always be accepted by a deterministic push-down automaton
- b)The union of two context free languages is context free
- c)The intersection of two contest free languages is a context free
- d)The complement of a context free language is a context free
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Which of the following statements is true?a)If a language is context f...
(A) is wrong as a language can be context free even if it is being accepted by non deterministic 
reverse}
(C) and (D) not always true as Context free languages are not closed under Complement and Intersection.
Most Upvoted Answer
Which of the following statements is true?a)If a language is context f...
Context Free Languages and Union
Context Free Language
A context-free language is a type of formal language that is generated by a context-free grammar. These are languages that can be parsed by a deterministic pushdown automaton (DPDA), which is an extension of a deterministic finite automaton (DFA).
Union of Two Context Free Languages
The union of two context-free languages is a new language that contains all the strings that are in either one of the languages. The statement "The union of two context-free languages is context-free" is true.
The proof of this statement involves constructing a new context-free grammar that generates the union of the two given context-free languages. This can be done by introducing a new start symbol and adding productions that generate the strings of the two languages separately.
For example, if L1 and L2 are two context-free languages with grammars G1 and G2, respectively, then the union of L1 and L2, denoted by L1 ∪ L2, can be generated by the following grammar:
S → S1 | S2
S1 → G1
S2 → G2
This grammar generates all the strings that are in either L1 or L2, since the start symbol S can be rewritten as S1 or S2, which generate the strings of L1 and L2, respectively.
Therefore, the union of two context-free languages is context-free, since it can be generated by a context-free grammar.
Conclusion
In summary, the statement "The union of two context-free languages is context-free" is true. This is because a new context-free grammar can be constructed that generates the union of the two given context-free languages.
Context Free Language
A context-free language is a type of formal language that is generated by a context-free grammar. These are languages that can be parsed by a deterministic pushdown automaton (DPDA), which is an extension of a deterministic finite automaton (DFA).
Union of Two Context Free Languages
The union of two context-free languages is a new language that contains all the strings that are in either one of the languages. The statement "The union of two context-free languages is context-free" is true.
The proof of this statement involves constructing a new context-free grammar that generates the union of the two given context-free languages. This can be done by introducing a new start symbol and adding productions that generate the strings of the two languages separately.
For example, if L1 and L2 are two context-free languages with grammars G1 and G2, respectively, then the union of L1 and L2, denoted by L1 ∪ L2, can be generated by the following grammar:
S → S1 | S2
S1 → G1
S2 → G2
This grammar generates all the strings that are in either L1 or L2, since the start symbol S can be rewritten as S1 or S2, which generate the strings of L1 and L2, respectively.
Therefore, the union of two context-free languages is context-free, since it can be generated by a context-free grammar.
Conclusion
In summary, the statement "The union of two context-free languages is context-free" is true. This is because a new context-free grammar can be constructed that generates the union of the two given context-free languages.
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Community Answer
Which of the following statements is true?a)If a language is context f...
(A) is wrong as a language can be context free even if it is being accepted by non deterministic
reverse}
(C) and (D) not always true as Context free languages are not closed under Complement and Intersection.
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Which of the following statements is true?a)If a language is context free it can always be accepted by a deterministic push-down automatonb)The union of two context free languages is context freec)The intersection of two contest free languages is a context freed)The complement of a context free language is a context freeCorrect answer is option 'B'. Can you explain this answer?
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