Important Properties

• \(\cap\) and \(\cup\) are commutative (Order does not matter) and associative (move parens around)

• Distribution:

\[ A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\\ A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \] - De Morgan’s law:

\[ (A \cap B)^c = A^c \cup B^c\\ (A \cup B)^c = A^c \cap B^c \]