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:

$$(A \cap B)^c = A^c \cup B^c\\ (A \cup B)^c = A^c \cap B^c$$