Boolean Algebra Cheat Sheet

Apr 20, 2020 #math #computer-science #discrete-mathematics

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

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