basic laws of sets

law	conditions
Idempotent law	$A \cup A = A \\ A \cap A = A$
Commutative law	$A \cup B = B \cup A \\ A \cap B = B \cap A$
Associative law	$(A \cup B) \cup C = A \cup (B \cup C ) \\ (A \cap B) \cap C = A \cap (B \cap C )$
Distributive law	$A \cup (B \cap C) = ( A \cup B) \cap ( A \cup C) \\ A \cap (B \cup C) = ( A \cap B) \cup ( A \cap C)$
DeMorgan's law	$( A \cup B )^c = A^c \cap B^c \\ ( A \cap B )^c = A^c \cup B^c$
identity law	$A \cup \emptyset = A \\ A \cap \emptyset = \emptyset \\ A \cup U = U \\ A \cap U = A$
compliment law	$A \cup A^c = U \\ A \cap A^c = \emptyset \\ U^c = \emptyset \\ \emptyset^c = U$
involution law	$( A^c)^c = A$