Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following types of languages:L1 ...
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Consider the following types of languages:
L1 Regular,
L2: Context-free,
L3: Recursive,
L4: Recursively enumerable.
L2: Context-free,
L3: Recursive,
L4: Recursively enumerable.
Q. Which of the following is/are TRUE?
I. L3' U L4 is recursively enumerable
II. L2 U L3 is recursive
III. L1* U L2 is context-free
IV. L1 U L2' is context-free
II. L2 U L3 is recursive
III. L1* U L2 is context-free
IV. L1 U L2' is context-free
- a)I only
- b)I and III only
- c)I and IV only
- d)I, II and III only
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following types of languages:L1 Regular,L2: Context-free,...
St 1: As L3 is Recursive and recursive languages are closed under complementation, L3’ will also be recursive. L3’ U L4 is also recursive as recursive languages are closed under union.
St 2: As L2 is Context- Free, it will be recursive as well. L2 U L3 is recursive because as recursive languages are closed under union.
St 3: L1* is regular because regular languages are closed under kleene –closure. L1* U L2 is context free as union of regular and context free is context free.
St 4: L2’ may or may not be context free because CFL are not closed under complementation. So it is not true. So I, II and III are correct.
St 2: As L2 is Context- Free, it will be recursive as well. L2 U L3 is recursive because as recursive languages are closed under union.
St 3: L1* is regular because regular languages are closed under kleene –closure. L1* U L2 is context free as union of regular and context free is context free.
St 4: L2’ may or may not be context free because CFL are not closed under complementation. So it is not true. So I, II and III are correct.
Most Upvoted Answer
Consider the following types of languages:L1 Regular,L2: Context-free,...
Types of Languages:
There are four types of formal languages in computer science:
L1 Regular
L2: Context-free
L3: Recursive
L4: Recursively enumerable
Solutions:
I. L3 U L4 is recursively enumerable:
- L3: Recursive languages can be decided by a Turing machine.
- L4: Recursively enumerable languages can be recognized by a Turing machine.
- Hence, L3 U L4 can be recognized by a Turing machine.
- Therefore, L3 U L4 is recursively enumerable.
II. L2 U L3 is recursive:
- L2: Context-free languages can be recognized by a Pushdown automaton.
- L3: Recursive languages can be decided by a Turing machine.
- Union of the two languages cannot be recognized by any automaton.
- Hence, L2 U L3 is not recursive.
III. L1* U L2 is context-free:
- L1*: Kleene closure of regular languages is regular.
- L2: Context-free languages can be recognized by a Pushdown automaton.
- Union of a regular language and a context-free language is always context-free.
- Hence, L1* U L2 is context-free.
IV. L1 U L2 is context-free:
- L1: Regular languages can be recognized by a Finite automaton.
- L2: Context-free languages can be recognized by a Pushdown automaton.
- Union of a regular language and a context-free language is always context-free.
- Hence, L1 U L2 is context-free.
Therefore, the correct option is D) I, II, and III only.
There are four types of formal languages in computer science:
L1 Regular
L2: Context-free
L3: Recursive
L4: Recursively enumerable
Solutions:
I. L3 U L4 is recursively enumerable:
- L3: Recursive languages can be decided by a Turing machine.
- L4: Recursively enumerable languages can be recognized by a Turing machine.
- Hence, L3 U L4 can be recognized by a Turing machine.
- Therefore, L3 U L4 is recursively enumerable.
II. L2 U L3 is recursive:
- L2: Context-free languages can be recognized by a Pushdown automaton.
- L3: Recursive languages can be decided by a Turing machine.
- Union of the two languages cannot be recognized by any automaton.
- Hence, L2 U L3 is not recursive.
III. L1* U L2 is context-free:
- L1*: Kleene closure of regular languages is regular.
- L2: Context-free languages can be recognized by a Pushdown automaton.
- Union of a regular language and a context-free language is always context-free.
- Hence, L1* U L2 is context-free.
IV. L1 U L2 is context-free:
- L1: Regular languages can be recognized by a Finite automaton.
- L2: Context-free languages can be recognized by a Pushdown automaton.
- Union of a regular language and a context-free language is always context-free.
- Hence, L1 U L2 is context-free.
Therefore, the correct option is D) I, II, and III only.
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Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer?
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Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 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 Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer?.
Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 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 Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following types of languages:L1 Regular,L2: Context-free,L3: Recursive,L4: Recursively enumerable.Q.Which of the following is/are TRUE?I. L3' U L4 is recursively enumerableII. L2 U L3 is recursiveIII. L1* U L2 is context-freeIV. L1 U L2' is context-freea)I onlyb)I and III onlyc)I and IV onlyd)I, II and III onlyCorrect answer is option 'D'. Can you explain this answer?.
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