COMPUTER SCIENCE AND ENGINEERING
THEORY OF COMPUTATION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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(a + b)
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(a + b) (a + b)*
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C.(a + b) (a + b)
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None of these
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Detailed explanation-1: -Two regular expressions are equivalent if languages generated by them are same. For example, (a+b*)* and (a+b)* generate same language. Every string which is generated by (a+b*)* is also generated by (a+b)* and vice versa.
Detailed explanation-2: -Regular expressions are equal if and only if they correspond to the same language. Thus for example ( a + b )* = ( a*b* )*, because they both represent the language of all strings over the alphabet a, b.
Detailed explanation-3: -Solution: As we know, any number of a’s means a* any number of b’s means b*, any number of c’s means c*. Since as given in problem statement, b’s appear after a’s and c’s appear after b’s. So the regular expression could be: R = a* b* c*
Detailed explanation-4: -So, a+b means [ab] or a|b, thus (a+b)* means any string of length 0 or more, containing any number of a s and b s in any order. Likewise, (a*b*)* also means any string of length 0 or more, containing any number of a s and b s in any order.