0 votes 0 votes Determine whether or not the following claims are true for all regular expressions r1 and r2. a) (r1*)* equivalent to r1* b) r1*(r1+r2)* equivalent to (r1+r2)* c) (r1+r2)* equivalent to (r1*r2*)* d) (r1r2)* equivalent to r1*r2* shouryarshi asked Aug 22, 2018 shouryarshi 615 views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply Lakshay Kakkar commented Aug 22, 2018 reply Follow Share All are true except option D. 0 votes 0 votes Lakshay Kakkar commented Aug 22, 2018 reply Follow Share The reason why D is wrong is because, RHS can also generate r1 and r2 separately, which however can't be generated by the LHS. 0 votes 0 votes Shaik Masthan commented Aug 22, 2018 reply Follow Share yes your reason is right.... but note that in the option D if one of the RE = epsilon then it is also true 0 votes 0 votes MiNiPanda commented Aug 22, 2018 reply Follow Share Shaik Masthan If both of them are ∅ then also it holds true as ∅* = ∈. Am i right? 0 votes 0 votes Lakshay Kakkar commented Aug 22, 2018 reply Follow Share @Shaik Masthan yes you are right. Just that the question asks 'for all regular expressions' I took the general case. 0 votes 0 votes Shaik Masthan commented Aug 22, 2018 reply Follow Share @MiNiPanda, yes... If both ( one ) of them are ∅ then also it holds true as ∅* = ∈. 0 votes 0 votes MiNiPanda commented Aug 22, 2018 reply Follow Share Shaik Masthan If r1= ∅ and r1=(ab)* then LHS : (r1r2)*= ( ∅ )*= ∈ RHS: r1*r2* = ( ∅ )* ((ab)*)* = ∈(ab)* = (ab)*=r2≠ LHS 0 votes 0 votes Shaik Masthan commented Aug 22, 2018 reply Follow Share sorry, didn't clearly comment... i want to convey the LHS only... but my bad didn't mention it 0 votes 0 votes Please log in or register to add a comment.