Question

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

Comments

i think answer should be C

take P = b^*

Q = b^prime

hence,R = b^*

so,P and R are regular but Q is not regular.

Answer 1

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

Comments

Last point

Ø.CFL = Ø ?

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when u concatenate any language with $\phi$, the result is always $\phi$