Set Identities

Associativity

$A \cup (B \cup C)=(A \cup B) \cup C$

$A \cap (B \cap C)=(A \cap B) \cap C$

Commutativity

$A \cup B = B \cup A$

$A \cap B = B \cap A$

Distributive

$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$

$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

Calculation is the knight who vanquishes Choice.