Set Operations

$A \cup \emptyset = A$	Identity laws
$A \cap U = A$
$A \cup U = U$	Domination laws
$A \cap \emptyset = \emptyset$
$A \cup A = A$	Idempotent laws
$A \cap A = A$

$\overline{(\overline{A})} = A$	Complementation law
$A \cup B = B \cup A$	Commutative laws
$A \cap B = B \cap A$
$(A \cup B) \cup C \equiv A \cup (B \cup C)$	Associative laws
$(A \cap B) \cap C \equiv A \cap (B \cap C)$
$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$	Distributive laws
$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

$\overline{A \cap B} = \overline{A} \cup \overline{B}$	De Morgan's laws
$\overline{A \cup B} = \overline{A} \cap \overline{B}$
$A \cup (A \cap B) = A$	Absorption laws
$A \cap (A \cup B) = A$

$A \cup \overline{A} = U$	Complement laws
$A \cap \overline{A} = \emptyset$

Exercises