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