MadeEasy Test Series closed

Question

Why option (b) is not equivalent to given regular expression?

Comments

b is right;

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https://gateoverflow.in/97112/equivalent-regex

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Even i feel tht option 'b'  should be the right answer

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RE=(a+b)*.(a+b+ ε).a

=(a+b)*aa  +  (a+b)*ba  +  (a+b)*a

=(a+b)*a (The remaining 2 terms are redundant).

This regular expression denotes the strings over {a,b}  such that the strings ending with a.The smallest possible string is a.

In option b) the RE is

RE=(( ε+a+b*)^+).a

This can be rewritten as

RE=  (ε+a+b*). (ε+a+b*)*.a

=(ε+a+b*).(a+b)*.a

=(a+b)*.a + a.(a+b)*.a + b*.(a+b)*.a

=(a+b)*.a (The remaining 2 terms are redundant).

Therefore the option b is same as the RE given in the question.

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The asked Reg expression is basically 'Strings whose end with a'

and yes option B too generate the same expression then certainly the answer is wrong .