Propiedades de los conjuntos

Sean $A$ , $B$ , y $C$ conjuntos cualesquiera y $U$ el conjunto universal, entonces:

$A \cap A = A$
$A \cup A = A$
$A \cap \emptyset = \emptyset$
$A \cup \emptyset = A$
$A \cap U = A$
$A \cup U = U$
$A \cap B = B \cap A$
$A \cup B = B \cup A$
$(A^{c})^{c} = A$
$(A \cap B) \cap C = A \cap (B \cap C)$
$(A \cup B) \cup C = A \cup (B \cup C)$
$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
$A \subseteq B \Leftrightarrow A \cap B = A$
$A \subseteq B \Leftrightarrow A \cup B = B$
$A \subseteq B \Leftrightarrow B^{c} \subseteq A^{c}$
$A \cap B \subseteq A \subseteq A \cup B$
$C - (A \cap B) = (C - A) \cup (C - B)$
$C - (A \cup B) = (C - A) \cap (C - B)$
$(B - A) \cup C = (B \cup C) - (A - C)$
$(B - A) \cap C = (B \cap C) - A$
$A \subseteq B \Leftrightarrow A - B = \emptyset$
$A \subseteq B = \emptyset \Leftrightarrow B - A = B$
$A - A = \emptyset$
$\emptyset - A = \emptyset$
$A - \emptyset = A$
$A - B = A \cap B^{c}$
$(B - A)^{c} = A \cup B^{c}$
$U - A = A^{c}$
$A - U = \emptyset$