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

Expression Equivalent To Name 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