Задача 13.

Prove that for any sets $A$, $B$, $C$ the following is true 1) $A\cup B=B\cup A$;  $A\cap B=B\cap A$; 2) $A\cup (B\cup C)=(A\cup B)\cup C$;  $A\cap (B\cap C)=(A\cap B)\cap C$; 3) $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$;  $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$ 4) $A\setminus (B\cup C)=(A\setminus B)\cap (A\setminus C)$;  $A\setminus (B\cap C)=(A\setminus B)\cup (A\setminus C)$.