Left quotient

If $L_1$ and $L_2$ are formal languages, then the left quotient of $L_1$ with $L_2$ is the language consisting of strings w such that xw is in $L_2$ for some string x in $L_1$. In symbols, we write:

$L_1 \backslash L_2 = \{w \ | \ \exists x ((x \in L_1) \land (xw \in L_2))\}$

You can regard the left quotient as the set of postfixes that complete words from $L_2$, such that the resulting word is in $L_1$.

For more details, see right quotient.