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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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 
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(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 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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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? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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