Application: Set Equivalences

Prove $A \cup (B \cup C) = (A \cup B) \cup C$

Prove $\overline{\overline{A}} = A$

Prove $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

Prove $\overline{A \cap B} = \overline{A} \cup \overline{B}$

Prove $A \subseteq B$ if and only if $\overline{B} \subseteq \overline{A}$