GATE Exam > GATE Questions > Consider the following statements:I.If L1 &cu...
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Consider the following statements:
I. If L1 ∪ L2 is regular, then both L1 and L2 must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE?
I. If L1 ∪ L2 is regular, then both L1 and L2 must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE?
- a)Neither I nor II
- b)II only
- c)I only
- d)Both I and II
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following statements:I.If L1 ∪ L2 is regular, then bo...
• If L1 ∪ L2 is regular, then neither needs to be regular.
Example: {anbn} ∪ {anbn}c = (a + b)* is regular but {anbn} and its complement both are non-regular.
So statement I is false.
• The class of regular language is not closed under infinite union.
Proof: It is was closed under infinite union then
anbn = {∈} ∪ {ab } ∪ {aabb } ∪ ........ will be infinite union of finite languages (which are regular) and hence will become regular. But we know that {anbn⏐n ≥ 0} is nonregular.
So II is false
So option (a), neither I nor II is the correct answer.
Example: {anbn} ∪ {anbn}c = (a + b)* is regular but {anbn} and its complement both are non-regular.
So statement I is false.
• The class of regular language is not closed under infinite union.
Proof: It is was closed under infinite union then
anbn = {∈} ∪ {ab } ∪ {aabb } ∪ ........ will be infinite union of finite languages (which are regular) and hence will become regular. But we know that {anbn⏐n ≥ 0} is nonregular.
So II is false
So option (a), neither I nor II is the correct answer.
Most Upvoted Answer
Consider the following statements:I.If L1 ∪ L2 is regular, then bo...
True.
If L1 is Turing-recognizable, then there exists a Turing machine that accepts all strings in L1. We can construct a Turing machine that simulates this Turing machine and then halts and accepts if the input is also in L2. This means that L1 ∩ L2 is Turing-recognizable.
If L1 is not Turing-recognizable, then we can still construct a Turing machine that simulates the Turing machine recognizing L1 and then rejects all strings in L2. This means that L1 ∩ L2 is not Turing-recognizable.
If L1 is Turing-recognizable, then there exists a Turing machine that accepts all strings in L1. We can construct a Turing machine that simulates this Turing machine and then halts and accepts if the input is also in L2. This means that L1 ∩ L2 is Turing-recognizable.
If L1 is not Turing-recognizable, then we can still construct a Turing machine that simulates the Turing machine recognizing L1 and then rejects all strings in L2. This means that L1 ∩ L2 is not Turing-recognizable.
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Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer?
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Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer?.
Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following statements:I.If L1 ∪ L2 is regular, then both L1 and L2 must be regular.II.The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)Neither I nor IIb)II onlyc)I onlyd)Both I and IICorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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