Language Concatenation

Definition

Language Concatenation

Let $L_{1}, L_{2}$ be two languages, then:
$L_{1} \cdot L_{2} = {w_{1} \cdot w_{2} ∣ w_{1} \in \land w_{2} \in L_{2}}$

A \cdot (B \cdot C) = (A \cdot B) \cdot C

A \cdot (B \cup C) = A \cdot B \cup A \cdot C

(B \cup C) \cdot A = B \cdot A \cup C \cdot A