P, Q, R are three languages. If P & R are regular and if PQ=R, then
A)Q has to be regular
B)Q cannot be regular
C)Q need not be regular
D)Q has to be a CFL

Question

Quizplus · Accepted Answer

Q need not necessarily be regular. The operation described does not guarantee that Q will inherit the regularity property from P and R. For instance, if P is a regular language that accepts all strings and R is also a regular language, Q could be any language (including non-regular ones) that satisfies the equation PQ = R, depending on the specific languages P and R.

P, Q, R Are Three Languages