Left quotient

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If L1 and L2 are formal languages, then the left quotient of L1 with L2 is the language consisting of strings w such that xw is in L1 for some string x in L2. In symbols, we write:

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

You can regard the left quotient as the set of postfixes that complete words from L2, such that the resulting word is in L1.

For more details, see right quotient.