I previously posted a logic rules cheat sheet and figured it was about time that I do the same for boolean algebra.

ExpressionEquivalent ToName of the Rule
$$X + Y$$$$Y + X$$Commutative
$$X \cdot Y$$$$Y \cdot X$$Commutative
$$(X + Y) + Z$$$$X + (Y + Z)$$Associative
$$(X \cdot Y) \cdot Z$$$$X \cdot (y \cdot Z)$$Associative
$$X + (Y \cdot Z)$$$$(X + Y) \cdot (Z + Z)$$Distributive
$$X \cdot (Y + Z)$$$$(X \cdot Y) + (X \cdot Z)$$Distributive
$$X + 0$$$$X$$Identity
$$X \cdot 1$$$$X$$Identity
$$X + X'$$$$1$$Complement
$$X \cdot X'$$$$0$$Complement
$$X + X$$$$X$$Idempotence
$$X \cdot X$$$$X$$Idempotence