Question

Please explain the answer shortly! :)

The language of the regular expression (0+10)* is the set of all strings of O's and 1's such that every 1 is immediately followed by a 0. Describe the complement of this language (with respect to the alphabet {0,1}) and identify in the list below the regular expression whose language is the complement of L((0+10)*). (0+1)*11(0+1)* (1+01)* (0+11)* (0+1)*1(8+1(0+1)*)

Answer 1

Ans) option D

Explaination:- to find the correct option let us take an example string and try to find which regular expression accepts it.

Let the strings be "1011".and "110" The regular expression we want must not accept any of these string as we want that regular expression that is complement of the expression that accepts string of 0's and 1's such that 1 is always followed by a 0.

option A i.e (0+1)*11(0+1)*. , this expression clearly accepts the string 1011. Therefore ruled out

option B i.e (1+01)* , this expression clearly accepts the string 1011. Therefore ruled out.

option C i.e (0+11)*, this expression clearly accepts the string 110. Therefore ruled out.

option D, i.e (0+1)*1(e + 1(0+1)*), this expression clearly does not accept the example strings that we have taken. Therefore it is the correct option.