a) $(A\cap B)\cap C=\left\{ x|x\in A\,\textrm{ và}\,x\in B \right\}\cap C$
$=\left\{ x|x\in A\,\textrm{ và}\,x\in B\textrm{ và}\,x\in C \right\}$
$=A\cap B\cap C$
$=A\cap (B\cap C)$
b) $A\cap (B\cup C)=A\cap \left\{ x|x\in B\textrm{ hoặc}\,x\in C \right\}$
$=\left\{ x|x\in A \right\}\cap \left\{ x|x\in B\textrm{ hoặc}\,x\in C \right\}$
$=\left\{ x|x\in A\,\textrm{và}\,x\in B \right\}\cup \left\{ x|x\in A\,\textrm{và}\,x\in C \right\}$
$=(A\cap B)\cup (A\cap C)$
c) $A\backslash (B\cup C)=A\backslash \left\{ x|x\in B\textrm{ hoặc}\,x\in C \right\}$
$=\left\{ x|x\in A\,\textrm{và}\,\,x\notin (B\textrm{ hoặc}\,C) \right\}$
$=\left\{ x|x\in A\,\textrm{và}\,x\notin B\textrm{ và}\,x\notin C \right\}$
$=\left\{ x|x\in A\,\textrm{và}\,x\notin B \right\}\,\cap \left\{ x|x\in A\,\textrm{và}\,x\notin C \right\}\,$
$=(A\backslash B)\,\cap (A\backslash C)\,$