1 votes 1 votes Let P,Q,R be 3 languages. If P and R are regular and if PQ=R, then a)Q has to be regular b)Q can not be regular c)Q need not be regular d)Q has to be CFL Sanjay Sharma asked Apr 15, 2017 Sanjay Sharma 4.1k views answer comment Share Follow See 1 comment See all 1 1 comment reply Akriti sood commented Apr 15, 2017 reply Follow Share i think answer should be C take P = b* Q = bprime hence,R = b* so,P and R are regular but Q is not regular. 3 votes 3 votes Please log in or register to add a comment.
Best answer 4 votes 4 votes P : Regular R : Regular P.Q = R Option B can directly eliminated : Q can be regular because if we concatenate two regular languages than their result is regular. Option D can also eliminated : Q need not be CFL , it can be regular also. option A can be eliminated :if we take Q as CFL. for eg: P : $\phi$ Q: $a^nb^n$ then R = $\phi$ which is regular. So option C is best akash.dinkar12 answered Apr 15, 2017 edited Jun 21, 2019 by akash.dinkar12 akash.dinkar12 comment Share Follow See all 2 Comments See all 2 2 Comments reply adm1n123 commented Oct 8, 2017 reply Follow Share Last point Ø.CFL = Ø ? 0 votes 0 votes akash.dinkar12 commented Oct 8, 2017 i edited by akash.dinkar12 Jun 21, 2019 reply Follow Share when u concatenate any language with $\phi$, the result is always $\phi$ 0 votes 0 votes Please log in or register to add a comment.