# Proving right quotient of two languages [duplicate]

I know that if a language $L_1$ and a language $L_2$ are regular, then $L1/L2$ is regular.

When we construct a DFA $M'=(Q, \Sigma, \delta, q_0, F)$, for each state $i$ we can make $i$ the start state (we'll represent is using $L'i$) and if $L'i \cap L_2 \neq 0$ then put $q_i$ in $F'$ in $M'$.

I understand the process of constructing an automaton M if both languages are regular, but what if L1 is regular but L2 is any language? How would I construct an automaton for this?

Thank you!

## marked as duplicate by Yuval Filmus, vonbrand, David Richerby, Rick Decker, JuhoFeb 15 '16 at 19:18

• What does $L'i$ denote? – DylanSp Feb 15 '16 at 14:22