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Consider the following regular expressions over the alphabet {0, 1}.
I. 1* 0(0 + 1)*
II. (0 + 1)* 01*
III. 1* 0(1 + 0)* + (0 + 1)* 01*
Which of the above regular expressions are equivalent?
  • a)
    I and III only
  • b)
    I and II only
  • c)
    II and III only
  • d)
    I, II and III
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following regular expressions over the alphabet {0, 1}.I....
I and II are quite easy to understand - both denote strings containing at least one 0. III is actually the union of I and II, but III is again denoting strings containing at least one 0, as both regular expressions (i.e. I and II) are equivalent, so union won't make any difference.
Hence all 3 regular expressions are equivalent.
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Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer?
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Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. 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 regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. 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 regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
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