Operations on a String

Length of a String
$| a b c | = 3$
$| ε | = 0$

Power Operator of a string
$a^{0} ≜ ε$
$a^{n + 1} ≜ a \dots a$ (n+1 times)

operation	associative	commutative	identity
union	yes	yes	$\nullset$
intersection	yes	yes	$Σ^{*}$
concatenation	yes	no	${ε}$

Quiz
$A \cdot (B \cup C) \qeq A B \cup A C$
$A \cdot (B \cap c) \qeq A B \cap A C$